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

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.

Create a FREE account and get:

Predict your JEE Main percentile, rank & performance in seconds

Check Your Score Now

Ask our AI anything

AI can make mistakes. Please verify important information.

Download resources