Multiple choice

Find the sum of the following geometric series: $1 + 4 + 16 + 64 +...... 9$ terms.

  1. $57381$
  2. $67381$
  3. $77381$
  4. $87381$
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D Correct answer
Explanation

This is a geometric series with a = 1, r = 4, n = 9. Sum = a(r^n - 1)/(r - 1) = 1(4^9 - 1)/(4 - 1) = (262144 - 1) / 3 = 262143 / 3 = 87381.

AI explanation

The given geometric series has a first term a = 1 and a common ratio r = 4. Using the geometric series sum formula, S_n = a(r^n - 1)/(r - 1), we substitute n = 9 to get S_9 = 1(4^9 - 1)/(4 - 1). Calculating 4^9 as 262144 gives (262144 - 1)/3 = 262143/3, which results in 87381.

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