Question

Can someone help me and explain this Algebra 2?

12. Describe an infinite geometric series with a beginning value of 2 that converges to 10. What are the first 4 terms of the series?

Answer 1

nth term of gp = a(1 - r^n)/(1 - r), where n∞ = 10, n = ∞, a = 2, r < 1
10 = 2(1 - r^∞)/(1 - r)
10 = 2/(1 - r)
1 - r = 2/10 = 1/5
r = 1 - 1/5 = 4/5
An infinite deometric series with a beginning value of 2 that converges to 10 has common ratio of 4/5.

The first four terms are: 2, 1.6, 1.28, 1.024