Question

Solve for the sum of series in given sequence

S(sub)5 in { 10, 30, 90, 270, 810, 2430}

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the sum of the series in the given sequence, we can use the formula for the sum of a geometric series:

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

where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, the first term (a) is 10, and the common ratio (r) is 3 (each term is obtained by multiplying the previous term by 3). The number of terms (n) is 5.

Plugging these values into the formula, we get:

S = 10 * (1 - 3^5) / (1 - 3)
= 10 * (1 - 243) / (1 - 3)
= 10 * (-242) / (-2)
= 10 * 121
= 1210

So the sum of the series S5 = { 10, 30, 90, 270, 810, 2430} is 1210.