Multiple choice

Find the number of terms in the series 1/81, - 1/27, 1/9, ….., 729.

  1. 9

  2. 11

  3. 15

  4. 17
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is a geometric progression with a = 1/81 and r = -3. The n-th term is a * r^(n-1) = 729. (1/81) * (-3)^(n-1) = 729. (-3)^(n-1) = 729 * 81 = 3^6 * 3^4 = 3^10. Since the term is positive, n-1 must be even. (-3)^10 = 3^10. n-1 = 10, so n = 11.

AI explanation

The sequence is a geometric progression with the first term as 1/81 and the common ratio as -3. Using the formula for the nth term, we set 729 equal to 1/81 multiplied by (-3) raised to the power of (n - 1). Solving (-3)^(n-1) = 59049 gives n - 1 = 10. The result is 11.

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