Geometric progression (term index): Find which term equals 1280. Series definition: 5, 10, 20, 40, … (each term doubles the previous). Determine the term number n for which the value is 1280. Choose the correct index.

Q: Geometric progression (term index): Find which term equals 1280. Series definition: 5, 10, 20, 40, … (each term doubles the previous). Determine the term number n for which the value is 1280. Choose the correct index.

Model tn = 5 × 2n−1. Solve for n 5 × 2n−1 = 12802n−1 = 1280 / 5 = 256 = 28n − 1 = 8 ⇒ n = 9 Final Answer 9th

Difficulty: Easy

10th
9th
8th
None of these

Correct Answer: 9th

Explanation:

Model
t_n = 5 × 2ⁿ⁻¹.

Solve for n
5 × 2ⁿ⁻¹ = 12802ⁿ⁻¹ = 1280 / 5 = 256 = 2⁸n − 1 = 8 ⇒ n = 9

Final Answer
9th

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