Recent questions tagged exercise9-3

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

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

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