Progression (Sequence and Series)Easy
Question
Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP is
Options
A.5
B.3/5
C.8/5
D.1/5
Solution
Let a = first term of G.P.
r = common ratio of G.P.; Then G.P. is a, ar, ar2
Given S∞ = 20 ⇒
= 20 ⇒ a = 20(1 - r) .....(i)
Also a2 + a2r2 + a2r4 + .... to ∞ = 100 ⇒
= 100 ⇒ a2 = 100(1 - r)(1 + r) .....(ii)
From (i), a2 = 400 (1-r)2 ; From (ii) and (iii), we get 100 (1 - r)(1+r) = 400 (1-r)2
⇒ 1 + r = 4 - 4r ⇒ 5r = 3 ⇒ r = 3/5
r = common ratio of G.P.; Then G.P. is a, ar, ar2
Given S∞ = 20 ⇒
= 20 ⇒ a = 20(1 - r) .....(i) Also a2 + a2r2 + a2r4 + .... to ∞ = 100 ⇒
= 100 ⇒ a2 = 100(1 - r)(1 + r) .....(ii) From (i), a2 = 400 (1-r)2 ; From (ii) and (iii), we get 100 (1 - r)(1+r) = 400 (1-r)2
⇒ 1 + r = 4 - 4r ⇒ 5r = 3 ⇒ r = 3/5
Create a free account to view solution
View Solution FreeMore Progression (Sequence and Series) Questions
If $a,b,c$ are in H.P., then $\left( \frac{1}{b} + \frac{1}{c} - \frac{1}{a} \right)\left( \frac{1}{c} + \frac{1}{a} - \...Consider the quadratic equation $\left( n^{2} - 2n + 2 \right)x^{2} - 3x + \left( n^{2} - 2n + 2 \right)^{2} = 0,n \in R...The sum $\sum_{k = 1}^{n}\mspace{2mu}\frac{k^{2} - \frac{1}{2}}{k^{4} + \frac{1}{4}}$ is equal to...Let ' $p$ ' be the first of ' $n$ ' arithmetic means between two positive numbers and ' $q$ ' be first of ' $n$ ' harmon...The value of x + y + z is 15 if a, x, y, z, b are in A.P. while the value of is if a, X, Y, Z, b are in H.P., then a and...