Question

Use the formula for the sum of the first n terms of each geometric sequence, and then state the indicated sum. Round your answer to the nearest hundredth.sigma, lower limit (a) 1, upper limit 11, starting value 64 times common ratio of 0.2 raised to a power of a-1S_5 = Answer

Answer 1

Given:

`\sum_{a\mathop{=}1}^(11)64\cdot(0.2)^(a-1)`

To find: Sum of first 5 terms

Step-by-step explanation:

Here, the first term is,

`a_1=64`

The common ratio, r = 0.2

The number of terms n = 5.

Using the sum formula for geometric series,

`S_n=(a_1(1-r^n))/(1-r)`

Substituting the values we get,

`\begin{gathered} S_5=(64(1-0.2^5))/(1-0.2) \\ =(64(1-0.2^(5)))/(1-0.2) \\ =79.97 \end{gathered}`

Thus, the sum of the first 5 terms is 79.97.

Final answer:

`S_5=79.97`