Sequences And Series Question 8
Question 8 - 2024 (29 Jan Shift 1)
If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to
(1) 7
(2) 4
(3) 5
(4) 6
Show Answer
Answer (4)
Solution
$a+a r+a r^{2}+a r^{3}+\ldots+a r^{63}$
$=7\left(a+a r^{2}+a r^{4} \ldots+a r^{62}\right)$
$\Rightarrow \frac{a\left(1-r^{64}\right)}{1-r}=\frac{7 a\left(1-r^{64}\right)}{1-r^{2}}$
$r=6$
