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

Answer:

The first term of the series is 125.

Step-by-step 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:

$203=x_{1} +x_{1}*0.4+x_{1}*(0.4)^{2} +x_{1}*(0.4)^{3}\\203 = (1+0.4+0.16+0.064)*x_{1}\\x_{1} = \frac{203}{1.624} \\x_{1} = 125$

The first term of the series is 125.