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Recent questions tagged sequences-and-series

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

If $a,b,c,d$ are in G.P, then show that $(a^2+b^2+c^2)(b^2+c^2+d^2)=(ab+bc+cd)^2$

asked Mar 3, 2014 by rvidyagovindarajan_1

1 answer

Show that the ratio of the first $n$ terms of a G.P. to the sum of the terms from $(n+1)^{th}$ to $(2n)^{th}$ term is $1:r^n$

asked Mar 2, 2014 by rvidyagovindarajan_1

1 answer

If the first and $n^{th}$ term of a G.P. are $a$ and $b$ respectively and if $P$ is the product of the $n$ terms then prove that $P^2=(ab)^n$

asked Mar 2, 2014 by rvidyagovindarajan_1

1 answer

If the $p^{th},q^{th}\:\:and\:\:r^{th}$ terms of G.P.are $a,b\:\:and\:\:c$ respectively then prove that $a^{q-r}.b^{r-p}.c^{p-q}=1$

asked Mar 1, 2014 by rvidyagovindarajan_1

1 answer

Find the four numbers forming a G.P. in which the $3^{rd}$ term is greater than the $1^{st}$ term by $9$ and the $2^{nd}$ term is greater than the $4^{th}$ term by $18$.

asked Mar 1, 2014 by rvidyagovindarajan_1

1 answer

Show that the product of the corresponding terms of the sequences $a,ar,ar^2.........ar^n$ and $A,AR,AR^2.............AR^{n-1}$ form a G.P. and find the common ratio.

asked Mar 1, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of the products of the corresponding terms of the sequences $2,4,8,.......32$ and $128,32,8,......\large\frac{1}{2}$

asked Mar 1, 2014 by rvidyagovindarajan_1

1 answer

Find the sum to $n$ terms of the sequence $8,88,888,.............$

asked Feb 27, 2014 by rvidyagovindarajan_1

1 answer

If the $4^{th},10^{th}\:\;and\:\:16^{th}$ terms of a G.P. are $x,y\:\;and\:\:z$ respectively. Prove that $x,y,z$ are in G.P.

asked Feb 27, 2014 by rvidyagovindarajan_1

1 answer

Find the G.P. the sum of whose first two terms is $-4$ and the $5^{th}$ term is $4$ times the $3^{rd}$ term.

asked Feb 27, 2014 by rvidyagovindarajan_1

1 answer

Given a G.P. with $a=729$ and $7^{th}$ term is $64$. Find $S_7.$

asked Feb 27, 2014 by rvidyagovindarajan_1

1 answer

The sum of first three terms of a G.P. is $16$ and the sum of next three terms is $128$. Find the $1^{st}$ term, common ratio and the sum of $n$ terms of the G.P.

asked Feb 26, 2014 by rvidyagovindarajan_1

1 answer

How many terms of the G.P. $3,3^2,3^3.......$ are needed to give the sum $120$?

asked Feb 26, 2014 by rvidyagovindarajan_1

1 answer

The sum of first $3$ terms of a G.P is $\large\frac{39}{10}$ and their product is $1$. Find the common ratio and the terms of the G.P.

asked Feb 26, 2014 by rvidyagovindarajan_1

1 answer

Evaluate $\sum\limits_{k=1}^{11} (2+3^k)$

asked Feb 26, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the G,P, $x^2,x^4,x^6...........$ in terms of $x$

asked Feb 26, 2014 by rvidyagovindarajan_1

1 answer

Find the sum up to $n$ terms of the G.P. $1,-a,a^2,-a^3.........$

asked Feb 26, 2014 by rvidyagovindarajan_1

1 answer

Find the sum upto $n$ terms of the G.P. $\sqrt 7,\sqrt {21},3\sqrt 7,.......$

asked Feb 26, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $20$ terms of the G.P., $0.15,0.015,0.0015................$

asked Feb 25, 2014 by rvidyagovindarajan_1

1 answer

For what value of $x$ the numbers $-\large\frac{2}{7},$$x,-\large\frac{7}{2}$ are in G.P.?

asked Feb 25, 2014 by rvidyagovindarajan_1

1 answer

Which term of the sequence $\large\frac{1}{3},\frac{1}{9},\frac{1}{27}.......$ is $\large\frac{1}{19683}$?

asked Feb 25, 2014 by rvidyagovindarajan_1

1 answer

Which term of the sequence $\sqrt 3,3,3\sqrt 3.......$ is $729?$

asked Feb 25, 2014 by rvidyagovindarajan_1

1 answer

Which term of the sequence $2,2\sqrt 2,4,.......\:\:is\:\:128?$

asked Feb 25, 2014 by rvidyagovindarajan_1

1 answer

The $4^{th}$ term of a G.P. is square of its second term, and the $1^{st}$ term is $-3$. Find its $7^{th}$ term.

asked Feb 25, 2014 by rvidyagovindarajan_1

1 answer

The $5^{th},8^{th}\:and\:11^{th}$ terms of a $G.P.$ are $p,q\:and\:s$ respectively. Show that $q^2=ps$

asked Feb 25, 2014 by rvidyagovindarajan_1

1 answer

Find the $12^{th}$ term of the $G.P.$ whose $8^{th}$ term is $192$ and common ratio=$2$

asked Feb 25, 2014 by rvidyagovindarajan_1

1 answer

Find the $20^{th}$ term of the $G.P.\:\:\large\frac{5}{2},\frac{5}{4},\frac{5}{8},..........$

asked Feb 25, 2014 by rvidyagovindarajan_1

1 answer

The difference between any two consecutive interior angles of a polygon is $5^\circ$. If the smallest angle is $120^ \circ$, then find the number of sides of the polygon.

asked Feb 24, 2014 by rvidyagovindarajan_1

1 answer

A man starts repaying a loan as first installment of $Rs.100$. If he increases the installment by $Rs.5$ every month, what amount he will pay in his $30^{th}$ installment?

asked Feb 24, 2014 by rvidyagovindarajan_1

1 answer

Between $1\:\:and\:\:31$ $m$ numbers are inserted so that the resulting sequence is an $A.P.$ and the ratio of $7^{th}\:\;and\:\:(m-1)^{th}$ numbers is $5:9$. find the value of $m$.

asked Feb 24, 2014 by rvidyagovindarajan_1

1 answer

If $\large\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$ is the $A.M.$ between $a$ and $b$, then find the value of $n$

asked Feb 24, 2014 by rvidyagovindarajan_1

1 answer

Insert $5$ numbers between $8\:and\:26$ such that the resulting sequence is an $A.P.$

asked Feb 23, 2014 by rvidyagovindarajan_1

1 answer

If the sum of $n$ terms of an $A.P.$ is $3n^2+5n$ and its $m^{th}$ term is $164$, find the value of $m$.

asked Feb 23, 2014 by rvidyagovindarajan_1

1 answer

The ratio of the sums of $m\:\:and\:\:n$ terms of an $A.P.$ is $m^2:n^2$. Show that the ratio of $m^{th}\:and\:n^{th}$ term is $(2m-1):(2n-1)$

asked Feb 23, 2014 by rvidyagovindarajan_1

1 answer

Sum of first $p,q\:\:and\:\:r\:terms$ of an $A.P.$ are $a,b\:\:and\:\:c$ respectively. Prove that $\large\frac{a}{p}$$(q-r)+\large\frac{b}{q}$$(r-p)+\large\frac{c}{r}$$(p-q)=0$

asked Feb 23, 2014 by rvidyagovindarajan_1

1 answer

If the sum of first $p$ terms of an $A.P.$ is equal to sum of first $q$ terms, then find the sum of first $p+q$ terms of the $A.P.$

asked Feb 23, 2014 by rvidyagovindarajan_1

1 answer

The sum of $n$ terms of two $A.P.s$ are in the ratio $5n+4:9n+6$ Find the ratio of their $18^{th}$ terms.

asked Feb 22, 2014 by rvidyagovindarajan_1

1 answer

If the sum of $n$ terms of an $A.P.$ is $(pn+qn^2)$ where $p$ and $q$ are constants, then find the common difference $d$.

asked Feb 22, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of an $A.P.$ whose $k^{th}$ term is $5k+1$

asked Feb 22, 2014 by rvidyagovindarajan_1

1 answer

If the sum of certain number of terms of the A.P., $25,22,19................$ is $116$, then find the last term.

asked Feb 20, 2014 by rvidyagovindarajan_1

1 answer

In an $A.P.$ if $p^{th}$ term is $\large\frac{1}{q}$ and $q^{th}$ term is $\large\frac{1}{p}$, then prove that the sum of first $pq$ terms is $\large\frac{1}{2}$$(pq+1)$ where $p\neq q$

asked Feb 20, 2014 by rvidyagovindarajan_1

1 answer

How many terms of the A.P. $-6,-\large\frac{11}{2}$$, -5........$ are needed to give the sum $-25$

asked Feb 20, 2014 by rvidyagovindarajan_1

1 answer

In an $A.P.$ the first term is $2$ and the sum of first $5$ terms is one-fourth of the next five terms. Find its $20^{th}$ term.

asked Feb 19, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of all the natural numbers lying between $100\:\: and\:\: 1000$ which are multiples of $5$

asked Feb 19, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of odd integers from $1 $ to $2001$

asked Feb 18, 2014 by rvidyagovindarajan_1

1 answer

The Fibanocci sequence is defined by $1=a_1=a_2\:\:and\:\:a_n=a_{n-1}+a_{n-2}\:\:for\:n>2$ Find $\large\frac{a_{n+1}}{a_n}$, for $n=1,2,3,4,5$

asked Feb 18, 2014 by rvidyagovindarajan_1

1 answer

Find the first $5$ terms of the series given by $a_1=a_2=2,\:a_n=a_{n-1}-1\:\:for\:\:n>2$

asked Feb 18, 2014 by rvidyagovindarajan_1

1 answer

Write the first five terms of the sequence given by $a_1=-1,\:a_n=\large\frac{a_{n-1}}{n}$$\:for\:n\geq 2$

asked Feb 18, 2014 by rvidyagovindarajan_1

1 answer

Find the first five terms of the sequence given by $a_1=3,\:a_n=3a_{n-1}+2\:\:\forall \:n\in N\:and\:n>1$

asked Feb 18, 2014 by rvidyagovindarajan_1

1 answer

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