Question

The first two terms in a geometric series are 20, 22. To two decimal places, the sum of the first k terms of the series is 271.59. Find k.​

Answer 1

k=9

Explanation:

First find r=22/20=1.1

The sum of the first k terms formula is a1•(1-r^k)/(1-r)

a1=20 and the sum is 271.59

Now plug in these values in the formula and find k.

271.59=20(1-1.1^k)/(1-1.1)

When you simplify this equation, you will get k=ln(2.358)/ln(1.1)

k=9