The first term of a G.P. is 1. The sum of the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $r$ be the common ratio of the $G.P.$The first term is $a = 1$.The $n^{th}$ term of a $G.P.$ is given by $a_n = a r^{n-1}$.Thus,the third term

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(B) Let $r$ be the common ratio of the $G.P.$The first term is $a = 1$.The $n^{th}$ term of a $G.P.$ is given by $a_n = a r^{n-1}$.Thus,the third term is $a_3 = a r^{3-1} = 1 \cdot r^2 = r^2$.The fifth term is $a_5 = a r^{5-1} = 1 \cdot r^4 = r^4$.Given that the sum of the third and fifth terms is $90$,we have:$r^2 + r^4 = 90$Rearranging the equation,we get:$r^4 + r^2 - 90 = 0$Let $x = r^2$. Then the equation becomes:$x^2 + x - 90 = 0$Factoring the quadratic equation:$(x + 10)(x - 9) = 0$This gives $x = -10$ or $x = 9$.Since $x = r^2$,$r^2$ cannot be negative for real numbers. Therefore,$r^2 = 9$.Taking the square root,we get $r = \pm 3$.

The first term of a $G.P.$ is $1$. The sum of the third and fifth terms is $90$. Find the common ratio of the $G.P.$ (in $, -3$)

Similar Questions

If $a_1, a_2, a_3, .... a_{21}$ are in $A.P.$ and $a_3 + a_5 + a_{11} + a_{17} + a_{19} = 10$,then the value of $\sum_{r=1}^{21} a_r$ is:

If the $A.M.$ between $p^{th}$ and $q^{th}$ terms of an $A.P.$ is equal to the $A.M.$ between $r^{th}$ and $s^{th}$ terms of the same $A.P.$,then $p + q$ is equal to

If the sum of three numbers of an arithmetic sequence is $15$ and the sum of their squares is $83$,then the numbers are

If $a, b, c$ are the $p^{th}, q^{th}$ and $r^{th}$ terms of a $G.P.$,then $\left( \frac{c}{b} \right)^p \left( \frac{b}{a} \right)^r \left( \frac{a}{c} \right)^q$ is equal to

The first term of a $G.P.$ is $7$,the last term is $448$,and the sum of all terms is $889$. Then the common ratio is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module