Question

Determine the number of terms, n, given the geometric series 1 3 9 27 ... and sn=3280.

Answer 1

The number of terms, 'n' is 8

How to determine the number of terms

Let's determine the common ratio;

common ratio, r = 3/1 = 3

The formula for sum of geometric series with 'r' greater than 1 is given as;  Sn = a( r^n - 1) / (r - 1)

n is unknown

Sn = 3280

Substitute the value

3280 = 1 ( 3^n - 1) / 3- 1

3280 = 3^n -1 /2

Cross multiply

3280 × 2 = 3^n - 1

6560 + 1 = 3^n

6561 = 3^n

This could be represented as;

3^8 = 3^n

like coefficient cancels out

n = 8

Thus, the number of terms, 'n' is 8

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