Question

Given the formula, Sn=a 1-r^n/1-r, what is the sum of the first nine terms of the geometric series: 324, -108, 36, -12...

If necessary, round to the hundredths place. (2 places after the decimal)

Answer 1

243.01.

Explanation:

The first term (a) = 324.

The common ratio (r) = -108/324 = -1/3.

So sum of 9 terms is:

S(9) = 324 * (1 - (-1/3)^9) / ( 1 - (-1/3)

= 324 ( 1 - (-0.00005076)) / 4/3

= 324 * 1.00005076 / 1.33333

= 243.012.