Question

An infinite geometric series contains consecutive terms 262.4, 209.92, 167.963 and the sum is 1640. What is the first term?​

Answer 1

328

Explanation:

`(a)/(1-r)` is the equation for the sum of an infinite geometric series, where
`a` is the first term of the infinite geometric series, and r is the common ratio between the terms. Here, we can find the common ratio between any consecutive terms.
`(209.92)/(262.4) = (4)/(5)`

Therefore,
`(a)/(1-(4)/(5)) = 1640`.

This simplifies to
`5a = 1640`

Therefore,
`a = 328`