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Recent questions tagged sequences-and-series
Questions
$150$ workers were engaged to finish a job in certain no. of days. $4$ workers dropped out on second day. $4$ more workers dropped out on third day and so on. It took $8$ more days to finish the work. Find the no. of days in which the work was completed.
cbse
class11
ch9
misc
bookproblem
sequences-and-series
sec-c
difficult
q32
math
asked
Apr 11, 2014
by
rvidyagovindarajan_1
1
answer
A manufacturer reckons that the value of a machine which costs him $Rs.15,625$, will depreciate each year by $20\%$. find the estimated value at the end of $5$ years.
cbse
class11
ch9
misc
bookproblem
sequences-and-series
sec-b
easy
q31
math
asked
Apr 11, 2014
by
rvidyagovindarajan_1
1
answer
A man deposited $Rs. 10,000$ in a bank at the rate of $5\%$ simple interest annually. Find the amount in $15^{th}$ year since he deposited the amount and also find the total amount after $20$ ears.
cbse
class11
ch9
misc
bookproblem
sequences-and-series
medium
sec-b
math
asked
Apr 10, 2014
by
rvidyagovindarajan_1
1
answer
A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with the instruction that they move the chain similarly. Assuming that the chain is not broken, and that it costs 50 paise to mail one letter, find the amount spent on the postage when $8^{th}$ set of letter is mailed.
cbse
class11
ch9
misc
bookproblem
sec-b
easy
q29
sequences-and-series
math
asked
Apr 9, 2014
by
rvidyagovindarajan_1
1
answer
Shamshad Ali buys a scooter for Rs. 22,000. He pays Rs. 4,000 cash and agrees to pay the balance in annual installment of Rs. 1,000 plus 10% interest on the unpaid amount. How much will the scooter costs him?
cbse
class11
ch9
bookproblem
easy
sec-c
misc
q28
math
sequences-and-series
asked
Apr 9, 2014
by
rvidyagovindarajan_1
1
answer
A farmer buys a used tractor for Rs. 12,000. He pays Rs. 6,000 cash and agrees to pay the balance in annual installments of Rs. 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?
cbse
class11
ch9
bookproblem
misc
easy
sec-b
q27
math
sequences-and-series
asked
Apr 8, 2014
by
rvidyagovindarajan_1
1
answer
Show that $\large\frac{1\times2^2+2\times 3^2+........n\times (n+1)^2}{1^2\times 2+2^2\times 3+.........n^2\times (n+1)}=\frac{3n+5}{3n+1}$
cbse
class11
ch9
bookproblem
sequences-and-series
misc
sec-c
difficult
q26
math
asked
Apr 7, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of $n$ terms of the series $3+7+13+21+31+.............$
cbse
class11
ch9
bookproblem
misc
medium
sec-c
q23
math
sequences-and-series
asked
Apr 2, 2014
by
rvidyagovindarajan_1
1
answer
Find the $20^{th}$ term of the series $2\times 4+4\times 6+6\times 8+..........$
cbse
class11
ch9
bookproblem
misc
sec-a
easy
q22
math
sequences-and-series
asked
Apr 2, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of $n$ terms of the series $\large\frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+.........$
cbse
class11
ch9
bookproblem
misc
sec-c
difficult
q25
math
sequences-and-series
asked
Apr 2, 2014
by
rvidyagovindarajan_1
1
answer
If $S_1,S_2,S_3$ are the sum of $n$ natural numbers,sum of their squares and sum of their cubes respectively then Show that $9S_2^2=S_3(1+8S_1)$
cbse
class11
ch9
bookproblem
misc
sec-a
medium
q24
math
sequences-and-series
asked
Apr 2, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of $n$ terms of the series $0.6+0.66+0.666+......$
cbse
class11
ch9
bookproblem
misc
medium
sec-b
q21-2
math
sequences-and-series
asked
Apr 2, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of the series $5+55+555+..........$ upto $n$ terms.
cbse
class11
ch9
bookproblem
misc
medium
sec-b
q21-1
math
sequences-and-series
asked
Apr 2, 2014
by
rvidyagovindarajan_1
1
answer
If $a,b,c$ are in A.P., $b,c,d$ are in G.P. and $\large\frac{1}{c},\frac{1}{d},\frac{1}{e}$ are in A.P., then prove that $a,c,e$ are in G.P.$
cbse
class11
ch9
bookproblem
misc
sec-b
medium
q20
math
sequences-and-series
asked
Apr 2, 2014
by
rvidyagovindarajan_1
1
answer
The ratio of A.M. and G.M. of two positive numbers $a$ and $b$ is $m:n$. Show that $a:b=(m+\sqrt {m^2-n^2}):(m-\sqrt {m^2-n^2})$
cbse
class11
ch9
bookproblem
misc
difficult
sec-c
q19
math
sequences-and-series
asked
Mar 31, 2014
by
rvidyagovindarajan_1
1
answer
If $a$ and $b$ are roots of $x^2-3x+p=0$ and $c$ and $d$ are roots of $x^2-12x+q=0$, where $a,b,c,d$ form a G.P. then prove that $(q+p):(q-p)=17:15$
cbse
class11
ch9
bookproblem
misc
difficult
sec-c
q18
math
sequences-and-series
asked
Mar 31, 2014
by
rvidyagovindarajan_1
1
answer
If $a,b,c,d$ are in G.P. then show that $(a^n+b^n),(b^n+c^n),(c^n+d^n)$ are in G.P.
cbse
class11
ch9
bookproblem
sec-b
difficult
misc
q17
math
sequences-and-series
asked
Mar 31, 2014
by
rvidyagovindarajan_1
1
answer
If $a\bigg(\large\frac{1}{b}+\frac{1}{c}\bigg)$$,\:b\bigg(\large\frac{1}{c}+\frac{1}{a}\bigg)$$,\:c\bigg(\large\frac{1}{a}+\frac{1}{b}\bigg)$ are in A.P., then prove that $a,b,c$ are in A.P.
cbse
class11
ch9
bookproblem
misc
difficult
sec-b
q16
math
sequences-and-series
asked
Mar 31, 2014
by
rvidyagovindarajan_1
1
answer
If $p^{th},\:q^{th}\:\:and\:\:r^{th}$ terms oa an A.P. are $a,\:b\:and\:c$ respectively, then show that $(q-r)a+(r-p)b+(p-q)c=0$
cbse
class11
ch9
misc
bookproblem
medium
sec-b
q15
math
sequences-and-series
asked
Mar 31, 2014
by
rvidyagovindarajan_1
1
answer
Let $S$ be the sum, $P$ the product and $R$ the sum of reciprocals of $n$ terms of a G.P. Prove that $P^2R^n=S^n$
cbse
class11
ch9
bookproblem
misc
difficult
sec-c
q14
math
sequences-and-series
asked
Mar 31, 2014
by
rvidyagovindarajan_1
1
answer
If $\large\frac{a+bx}{a-bx}=\frac{b+cx}{b-cx}=\frac{c+dx}{c-dx}$$\:(x\neq0)$, then show that $a,b,c\:and\:d$ are in G.P.
cbse
class11
ch9
bookproblem
misc
difficult
sec-b
q13
math
sequences-and-series
asked
Mar 30, 2014
by
rvidyagovindarajan_1
1
answer
The sum of first four terms of an A.P. is $56$. The sum of last four terms is $112$. If its first term is $11$ then find the number of terms.
cbse
class11
ch9
bookproblem
misc
sec-b
medium
q12
math
sequences-and-series
asked
Mar 30, 2014
by
rvidyagovindarajan_1
1
answer
A G.P. consists of even number of terms. If the sum of all the numbers is $5$ times the sum of terms occupying the odd places, then find the common ratio.
cbse
class11
ch9
bookproblem
misc
sec-b
difficult
q11
math
sequences-and-series
asked
Mar 30, 2014
by
rvidyagovindarajan_1
1
answer
The sum of three numbers in G.P. is $56$. If we subtract $1,7,21$ from the numbers in that order, we obtain an A.P. Find the numbers.
cbse
class11
ch9
bookproblem
sec-b
medium
misc
q10
math
sequences-and-series
asked
Mar 30, 2014
by
rvidyagovindarajan_1
1
answer
The first term of a G.P. is $1$. The sum of third term and fifth term is $90$. Find the common ratio of the G.P.
cbse
class11
ch9
bookproblem
misc
sec-b
easy
q9
math
sequences-and-series
asked
Mar 30, 2014
by
rvidyagovindarajan_1
1
answer
The sum of some terms of a G.P. is $315$ whose first term and the common ratio are $5$ and $2$ respectively. Find the last term and number of terms of the series.
cbse
class11
ch9
bookproblem
misc
sec-b
easy
q8
math
sequences-and-series
asked
Mar 30, 2014
by
rvidyagovindarajan_1
1
answer
If $f$ is a function satisfying $f(x+y)=f(x).f(y)\:\:\forall x,y\in N$ such that $f(1)=3\:\:and\:\:\displaystyle\sum ^{n}_{x=1} f(x)=120$, then find the value of $n$.
cbse
class11
ch9
bookproblem
misc
sec-b
medium
q7
math
sequences-and-series
asked
Mar 29, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of all two digit numbers which when divided by $4$ yields $1$ as remainder.
cbse
class11
ch9
bookproblem
misc
sec-b
easy
q6
math
sequences-and-series
asked
Mar 29, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of all the integers from $1$ and $100$ that are divisible by $2$ or $5$.
cbse
class11
ch9
bookproblem
misc
medium
sec-b
q5
math
sequences-and-series
asked
Mar 29, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of all the numbers between $200$ and $400$ which are divisible by $7$.
cbse
class11
ch9
bookproblem
misc
medium
sec-b
q4
math
sequences-and-series
asked
Mar 28, 2014
by
rvidyagovindarajan_1
1
answer
If the sum of $n,2n\:and\:3n$ terms of an A.P. are $S_1,S_2\:and\:S_3$ respectively, then show that $S_3=3(S_2-S_1)$
cbse
class11
ch9
bookproblem
misc
medium
sec-b
q3
math
sequences-and-series
asked
Mar 28, 2014
by
rvidyagovindarajan_1
1
answer
If the sum of three numbers in A.P. is $24$ and their product is $440$, then find the numbers.
cbse
class11
ch9
bookproblem
misc
easy
sec-b
q2
math
sequences-and-series
asked
Mar 28, 2014
by
rvidyagovindarajan_1
1
answer
Show that the sum of $(m+n)^{th}$ and $(m-n)^{th}$ terms of an A.P is twice its $m^{th}$ term.
cbse
class11
ch9
misc
bookproblem
sec-a
easy
q1
math
sequences-and-series
asked
Mar 27, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of $n$ terms of the series whose $n^{th}$ term is $(2n-1)^2$
cbse
class11
ch9
bookproblem
exercise9-4
sec-b
easy
q10
math
sequences-and-series
asked
Mar 27, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of $n$ terms of the series whose $n^{th}$ term is given by $n^2+2^n$.
cbse
class11
ch9
bookproblem
exercise9-4
medium
sec-b
q9
math
sequences-and-series
asked
Mar 24, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of $n$ terms of the series whose $n^{th}$ term is given by $n(n+1)(n+4)$
cbse
class11
ch9
bookproblem
exercise9-4
easy
sec-b
q8
math
sequences-and-series
asked
Mar 24, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum to $n$ terms of the series $1^2+(1^2+2^2)+(1^2+2^2+3^2)+........$
cbse
class11
ch9
bookproblem
exercise9-4
medium
sec-c
q7
math
sequences-and-series
asked
Mar 24, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of $n$ terms of the series $(3\times 8)+(6\times 11)+(9\times 14).............$
cbse
class11
ch9
bookproblem
exercise9-4
sec-c
medium
q6
math
sequences-and-series
asked
Mar 13, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of 20 terms of the series. $5^2+6^2+7^2+.....20^2$
cbse
class11
ch9
math
exercise9-3
sec-b
easy
q5
sequences-and-series
asked
Mar 12, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum to $n$ terms of the series $\large\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+..........$
cbse
class11
ch9
bookproblem
difficult
exercise9-4
sec-c
q4
math
sequences-and-series
asked
Mar 10, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of $n$ terms of the series $3\times 1^2+5\times 2^2+7\times 3^2+.........$
cbse
class11
ch9
bookproblem
exercise9-4
sec-c
medium
q3
math
sequences-and-series
asked
Mar 7, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of $n$ terms of the series $(1\times 2\times 3)+(2\times 3\times 4)+(3\times 4\times 5)+.......$
cbse
class11
ch9
bookproblem
exercise9-4
medium
sec-c
q2
math
sequences-and-series
asked
Mar 7, 2014
by
rvidyagovindarajan_1
1
answer
Find the sum of $n$ terms of the series $1\times 2+2\times 3+3\times 4+4\times 5+.............$
cbse
class11
ch9
bookproblem
exercise9-4
sec-b
medium
q1
math
sequences-and-series
asked
Mar 7, 2014
by
rvidyagovindarajan_1
1
answer
If A.M. and G.M. of roots of a quadratic equation are $8$ and $5$ respectively. Find the quadratic equation.
cbse
class11
ch9
bookproblem
exercise9-3
sec-a
easy
q32
math
sequences-and-series
asked
Mar 7, 2014
by
rvidyagovindarajan_1
1
answer
What will Rs. 500 amounts to in $10$ years after its deposit in a bank which pays annual interest of $10%$ compounded annually?
cbse
class11
ch9
bookproblem
exercise9-3
sec-b
easy
q31
math
sequences-and-series
asked
Mar 6, 2014
by
rvidyagovindarajan_1
1
answer
The number of bacteria in certain culture doubles every hour. If there were $30$ bacteria present in the culture originally, how many bacteria will be present at the end of $2^{nd}$ hour, $4^{th}$ hour and $n^{th}$ hour?
cbse
class11
ch9
bookproblem
exercise9-3
sec-a
easy
q30
math
sequences-and-series
asked
Mar 6, 2014
by
rvidyagovindarajan_1
1
answer
$ the A.M. and $G$ the G.M. between two positive numbers then show that the numbers are $A\pm \sqrt {(A+G)(A-G)}$
cbse
class11
ch9
bookproblem
exercise9-3
sec-c
difficult
q29
math
sequences-and-series
asked
Mar 6, 2014
by
rvidyagovindarajan_1
1
answer
The sum of two numbers is $6$ times their geometric mean.Show that the ratio of the numbers is $3+2\sqrt 2\::\:3-2\sqrt 2$
cbse
class11
ch9
bookproblem
exercise9-3
difficult
sec-c
q28
math
sequences-and-series
asked
Mar 5, 2014
by
rvidyagovindarajan_1
1
answer
Find the value of $n$ so that $\large\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ may be the geometric mean between $a$ and $b$.
cbse
class11
ch9
bookproblem
exercise9-3
difficult
sec-c
q27
math
sequences-and-series
asked
Mar 4, 2014
by
rvidyagovindarajan_1
1
answer
Insert $2$ numbers between $3$ and $81$ so that the resulting sequence is a G.P. Find the two numbers.
cbse
class11
ch9
bookproblem
exercise9-3
sec-a
easy
q26
math
sequences-and-series
asked
Mar 3, 2014
by
rvidyagovindarajan_1
1
answer
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