Multiple choice

How many terms of the series 1+3+9+......., sum to 1093?

  1. 5

  2. 6

  3. 7

  4. 3
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C Correct answer
Explanation

This is a geometric series with a=1, r=3. Sum = a(r^n - 1) / (r - 1). 1093 = 1(3^n - 1) / 2. 2186 = 3^n - 1. 2187 = 3^n. Since 3^7 = 2187, n = 7.

AI explanation

This is a geometric progression with the first term a = 1 and common ratio r = 3. The sum of n terms formula is S_n = a(r^n - 1) / (r - 1). Solving the equation 1093 = 1(3^n - 1) / 2 gives 2186 = 3^n - 1, meaning 3^n = 2187. Since 3^7 = 2187, exactly 7 terms are needed to sum to 1093.

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