Multiple choice

How many terms of the series 1+3+9+ ...sum to 364?

  1. 5

  2. 6

  3. 4

  4. 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is a geometric series with a=1, r=3. Sum = a(r^n - 1)/(r-1) = 1(3^n - 1)/2 = 364. 3^n - 1 = 728. 3^n = 729. Since 3^6 = 729, n = 6.

AI explanation

The series 1 + 3 + 9 + ... is a geometric progression with first term 1 and common ratio 3. The sum of n terms formula is a(r^n - 1)/(r - 1). Setting the sum to 364 gives (3^n - 1)/(3 - 1) = 364, so 3^n - 1 = 728 and 3^n = 729. Since 3^6 equals 729, there are 6 terms.

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