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:
[tex]S=x_{1} +x_{1}r+x_{1}r^{2} +x_{1}r^{3}[/tex]
Where x1 is the first term and r is the common ratio. Replacing the given values into the equation to solve for x1 yields:
[tex]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[/tex]
The first term of the series is 125.
