Question

The common ratio of a geometric series is 9, while the sum of the first 10 terms in the series is 435,848,050. What is the first term in the series? Responses A 99 B 191 9 C 11 D 81

Answer 1

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Explanation:

The sum of a finite geometric series is given by the formula:

Sum = a * (1 - r^n) / (1 - r)

Where a is the first term, r is the common ratio, and n is the number of terms in the series.

In this case, we are given that the sum is 435,848,050 and the common ratio is 9, and we want to find the first term a. We are also given that there are 10 terms in the series.

Substituting these values into the formula, we get:

435,848,050 = a * (1 - 9^10) / (1 - 9)

Solving for a, we get:

a = 435,848,050 * (1 - 9) / (1 - 9^10)

= 435,848,050 * (-8) / (-8)

= 435,848,050

Therefore, the first term in the series is a = 435,848,050.

The answer is therefore D: 81.