Use the formula for the sum of the first n terms of a geometric series to find S9 for the series 12, 6, 3, 3/2 , …

Use the formula for the sum of the first n terms of a geometric series to find S₉ for the series 12, 6, 3, 3/2 , …

Expert Solution

Consider the geometric series,

12, 6, 3, 3/2, …

First term of the series is a1 = 12.

Compute common ratio of the given series as follows:

r = a2/a1

= 6/12

= 1/2

Use the formula for the sum of first ‘n’ terms of a geometric series,

Sn = a1∙(1 – rn)/(1 – r) ...... (1)

Substitute n = 9, r = 1/2 and a1 = 12 in the formula (1) and simplify,

S9 = 12 × {1 – (1/2)9}/(1 – 1/2)

= 12 × {1 – 1/512}/1/2

= (12 × 511/512)/1/2

= 1533/64

Therefore, sum of first 9 terms of the given series is S9 = 1533/64.

Junaid answered 1 year ago

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