Question

Which term of the series 5, 10, 20, 40, ..... is 1280?

• A. 10th
• B. 8th
• C. 9th
• D. None of the above

Hint:

In geometric progressions, use the formula \( T_n = a \cdot r^{n-1} \) to find the \( n \)-th term. Ensure you correctly handle the powers of the common ratio.

Answer 1

The Correct Option is C

The given sequence is 5, 10, 20, 40, .... This is a geometric progression with the first term \( a = 5 \) and common ratio \( r = 2 \). The formula for the \( n \)-th term of a geometric progression is: \[ T_n = a \cdot r^{n-1} \] We are given that the \( n \)-th term is 1280. Substituting the values into the formula, we get: \[ 1280 = 5 \cdot 2^{n-1} \] Dividing both sides by 5: \[ 256 = 2^{n-1} \] Now, solving for \( n \): \[ 2^8 = 256 \Rightarrow n - 1 = 8 \Rightarrow n = 9 \] Thus, the 9th term of the sequence is 1280.