Question

Describe an infinite geometric series with the beginning value of 2 that converges to 10 what are the first four terms of the series

Answer 1

• an = 2·(4/5)^(n-1)
• 2, 8/5, 32/25, 128/125

Explanation:

The sum of an infinite geometric series is ...

S = a1/(1 -r)

where r is the common ratio. The sum will only exist if |r| < 1.

The problem statement tells us S = 10 and a1 = 2, so we have ...

10 = 2/(1 -r)

r = 1 -2/10 = 4/5

So the n-th term of the series is ...

an = a1·r^(n-1)

an = 2·(4/5)^(n-1)

For values of n = 1 to 4, the terms are ...

2, 8/5, 32/25, 128/125