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inessss [21]
2 years ago
8

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

Mathematics
1 answer:
tatuchka [14]2 years ago
8 0

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.

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