Multiple choice

If the first term in a geometric sequence is $3$, and if the third term is $48$, find the $11^{th}$ term.

  1. $228$
  2. $528$
  3. $110592$
  4. $3145728$
  5. $12582912$
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D Correct answer
Explanation

a = 3, ar^2 = 48 => r^2 = 16 => r = 4. 11th term = ar^10 = 3 * 4^10 = 3 * 1048576 = 3145728.

AI explanation

Using the geometric sequence formula a_n = a * r^(n-1), we know the first term is 3 and the third term is 48, so 3 * r^2 = 48. Solving for the common ratio r gives r^2 = 16, meaning r = 4. To find the 11th term, substitute a = 3, r = 4, and n = 11 into the formula to get 3 * 4^(11-1), which equals 3 * 4^10. Calculating 4^10 gives 1048576, and multiplying by 3 results in 3145728.

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