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.

k=9

Step-by-step 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