Questions

How many terms must be taken of: the series $\rm 32 + 48 + 72 + \dots $ to make the sum 665?

Find the sum of the geometric series: $\rm \sum_{n = 4}^{12}2(5)^{n - 4}$.

Find the sum of the geometric series: $\rm \sum_{n = 1}^{5} (3)^{n + 1}$.

Find the sum of the geometric series: $\rm \sum_{n = 3}^{8}2(-2)^{n}$.

Find the sum of the geometric series: $\rm \sum_{n = 3}^{5}3(4)^{n-2}$.

Find the number of terms and the common ratios of a geometric series when the first term is 3, the last term is 384 and the sum is 765.

Find the number of terms and the common ratios of a geometric series when the first term is 5, the last term is 320, and the sum is 635.

Find the number of terms and the common ratios of a geometric series when the first term is 2, the last term 486, and the sum 728.

Find the number of terms and the common ratios of a geometric series when the first term is 7, the last term 189, and the sum 280.

Find the sum of the sequence, $\rm 3^6, 3^5, 3^4, \dots ,$ to 15 terms.