Question 62

Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033, then the sum of these three terms is equal to

Name: Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033, then the sum of these three terms is equal to
Uploaded: 2026-06-02T17:37:41.570327+05:30
Duration: 2 min 58 s
Description: Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033, then the sum of these three terms is equal to

Solution

Let the GP be $$a, ar, ar^2$$ where $$a, r$$ are positive integers.

Sum of squares: $$a^2(1 + r^2 + r^4) = 33033$$

Factoring: $$33033 = 3 \times 7 \times 11^2 \times 13$$

Try $$r = 4$$: $$1 + 16 + 256 = 273 = 3 \times 7 \times 13$$

$$a^2 = 33033/273 = 121$$, so $$a = 11$$ ✓

Sum = $$a(1 + r + r^2) = 11(1 + 4 + 16) = 11 \times 21 = 231$$

The correct answer is Option 2: 231.

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Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033, then the sum of these three terms is equal to

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