Question

The sum of the first 10 terms of a geometric progression is 1023, and the first term is 1. What is the common ratio?

• A. 2
• B. 3
• C. 4
• D. 5

Hint:

Use the GP sum formula and test possible ratios to find the common ratio.

Answer 1

The Correct Option is A

- Step 1: For a GP, sum of first $n$ terms = $a \frac{r^n - 1}{r - 1}$. Given $a = 1$, $n = 10$, sum = 1023.
- Step 2: So, $\frac{r^{10} - 1}{r - 1} = 1023$.
- Step 3: Try $r = 2$: $\frac{2^{10} - 1}{2 - 1} = \frac{1024 - 1}{1} = 1023$, matches.
- Step 4: Verify: Terms are $1, 2, 4, \ldots, 512$, sum = $1 + 2 + 4 + \cdots + 512 = 1023$.
- Step 5: Check options: Option (1) is 2, correct.