Question
If the sum of an infinite GP a, a r, a r^2, a r^3, is 15 and the sum of the squares of its each term is 150 , then the sum of a r^2, a r^4, a r^6, is :
BITSAT
Mathematics
Sequences and Series
2023
BITSAT 2023 (Memory Based Paper 1)
BITSAT Mathematics Question (2023) — Solution
Options
- A. 5 2
- B. 1 2
- C. 25 2
- D. 9 2
Answer
B. 1 2
Step-by-step solution
Sum of infinite terms of series a +a r+a r^2+ =15 a 1-r =15 ...(i) Sequence formed by square of terms: a^2, a^2 r^2, a^2 r^4, a^2 r^6 a^2+a^2 r^2+ =150 Sum = a^2 1-r^2 =150 a 1-r a 1+r =15 15 a 1+r =150 ( a 1- r =15 ) a 1+r =10 ...(ii) On dividing equation (i) by (ii) 1+ r 1- r = 15 10 or r= 1 5 a=12 Now series : a r^2+a r^4+a r^6+ Sum = a^2 1-r^2 = 12 ( 1 25 ) 1- 1 25 = 1 2
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