Sequence And Series Question 169
Question: A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, then the common ratio will be equal to
Options:
A) 2
B) 3
C) 4
D) 5
Show Answer
Answer:
Correct Answer: C
Solution:
Correct option is C. 4
Let there be (2n) terms in the G.P. with first term (a) and common ratio (r).
Then,
Sum of all the terms = 5 (Sum of the terms occupying the odd places)
$\Rightarrow a_1 + a_2 + \ldots + a_{2n} = 5(a_1 + a_3 + a_5 + \ldots + a_{2n-1})$
$\Rightarrow a + ar + \ldots + ar^{2n-1} = 5(a + ar^2 + \ldots + ar^{2n-2})$
$\Rightarrow a \left{ \frac{1 - r^{2n}}{1 - r} \right} = 5a \left{ \frac{1 - (r^2)^n}{1 - r^2} \right}$
$\Rightarrow 1 + r = 5$
$\Rightarrow r = 4$
BETA
