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Recent questions tagged sequences-and-series

$150$ 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.

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.

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.

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.

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?

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?

asked Apr 8, 2014 by rvidyagovindarajan_1

1 answer

Show that $\large\frac{1\times2^2+2\times 3^2+........n\times (n+1)^2}{1^2\times 2+2^2\times 3+.........n^2\times (n+1)}=\frac{3n+5}{3n+1}$

asked Apr 7, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series $3+7+13+21+31+.............$

asked Apr 2, 2014 by rvidyagovindarajan_1

1 answer

Find the $20^{th}$ term of the series $2\times 4+4\times 6+6\times 8+..........$

asked Apr 2, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series $\large\frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+.........$

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 $9S_2^2=S_3(1+8S_1)$

asked Apr 2, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series $0.6+0.66+0.666+......$

asked Apr 2, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of the series $5+55+555+..........$ upto $n$ terms.

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.$

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 $a:b=(m+\sqrt {m^2-n^2}):(m-\sqrt {m^2-n^2})$

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 $(q+p):(q-p)=17:15$

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.

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.

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 $(q-r)a+(r-p)b+(p-q)c=0$

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 $P^2R^n=S^n$

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.

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.

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.

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.

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.

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.

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 $n$.

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.

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 $5$.

asked Mar 29, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of all the numbers between $200$ and $400$ which are divisible by $7$.

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 $S_3=3(S_2-S_1)$

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.

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.

asked Mar 27, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series whose $n^{th}$ term is $(2n-1)^2$

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 $n^2+2^n$.

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 $n(n+1)(n+4)$

asked Mar 24, 2014 by rvidyagovindarajan_1

1 answer

Find the sum to $n$ terms of the series $1^2+(1^2+2^2)+(1^2+2^2+3^2)+........$

asked Mar 24, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series $(3\times 8)+(6\times 11)+(9\times 14).............$

asked Mar 13, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of 20 terms of the series. $5^2+6^2+7^2+.....20^2$

asked Mar 12, 2014 by rvidyagovindarajan_1

1 answer

Find the sum to $n$ terms of the series $\large\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+..........$

asked Mar 10, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series $3\times 1^2+5\times 2^2+7\times 3^2+.........$

asked Mar 7, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series $(1\times 2\times 3)+(2\times 3\times 4)+(3\times 4\times 5)+.......$

asked Mar 7, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series $1\times 2+2\times 3+3\times 4+4\times 5+.............$

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.

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?

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?

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 $A\pm \sqrt {(A+G)(A-G)}$

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 $3+2\sqrt 2\::\:3-2\sqrt 2$

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 $b$.

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.

asked Mar 3, 2014 by rvidyagovindarajan_1

1 answer

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