Question

Complete the statements about series A and B. Series A: 10+4+ 8/5 + 16/25 + 32/125 + ... Series B: 1/5+ 3/5 + 9/5 + 27/5 + 81/5 + ... Series ____ has an r value of ___ where 0 < |r| < 1 . So, we can find the sum of the series. The sum of the series is ___.

Answer 1

Series "A" has an r value of "2/5" where 0 < |r| < 1 . So, we can find the sum of the series. The sum of the series is "50/3".

Answer 2

Series "A" has an r value of "2/5" where 0 < |r| < 1 . So, we can find the sum of the series. The sum of the series is "50/3".

Explanation:

To find the r (rate) of each series, we can divide one term by the term before:

Series A: 4 / 10 = 2/5

Series B: (3/5) / (1/5) = 3

So the series A has an r value between 0 and 1, so we can find the sum of the series.

The sum is given by the formula:

Sum = a1 / (1 - r)

Where a1 is the first term. So we have that:

Sum = 10 / (1 - (2/5))

Sum = 10 / (3/5)

Sum = 10 * (5/3) = 50/3