Single correct option
The sum of an infinite geometric progression is 54, and the sum of the squares of its terms is 1458. What is the third term of the progression?
- A. 2
- B. 4
- C. 6
- D. 8
Show answer and solution
Answer: (B) 4
Let first term a and ratio r (|r| < 1): a/(1 − r) = 54 and a²/(1 − r²) = 1458.
Divide the second by the first: a/(1 + r) = 1458/54 = 27.
So a = 54(1 − r) = 27(1 + r) → 54 − 54r = 27 + 27r → r = 1/3, a = 36.
Third term = a r² = 36 × 1/9 = 4.
Divide the second by the first: a/(1 + r) = 1458/54 = 27.
So a = 54(1 − r) = 27(1 + r) → 54 − 54r = 27 + 27r → r = 1/3, a = 36.
Third term = a r² = 36 × 1/9 = 4.
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