Question

The sum of the first four terms of a geometric series is 203, and the common ratio is 0.4. Find the first term

Answer 1

The first term of the series is 125.

Explanation:

The sum of the first four terms of a geometric series can be described by the following equation:

`S=x_(1) +x_(1)r+x_(1)r^(2) +x_(1)r^(3)`

Where x1 is the first term and r is the common ratio. Replacing the given values into the equation to solve for x1 yields:

`203=x_(1) +x_(1)*0.4+x_(1)*(0.4)^(2) +x_(1)*(0.4)^(3)\\203 = (1+0.4+0.16+0.064)*x_(1)\\x_(1) = (203)/(1.624) \\x_(1) = 125`

The first term of the series is 125.