Question

What is the approximate value of ? Round your answer to the nearest hundredth. 1.25 3.00 3.75 4.25

Answer 1

C

Explanation:

edge

Answer 2

Option C:

`\sum_(n=1)^(5) 3(0.2)^(n-1)=3.75`

Solution:

Given expression:

`\sum_(n=1)^(5) 3(0.2)^(n-1)`

Summation means sum of the numbers.

Put n = 1 to 5 and sum all the numbers.

`\sum_(n=1)^(5) 3(0.2)^(n-1)`

`=3(0.2)^(1-1)+3(0.2)^(2-1)+3(0.2)^(3-1)+3(0.2)^(4-1)+3(0.2)^(5-1)`

`=3(0.2)^(0)+3(0.2)^(1)+3(0.2)^(2)+3(0.2)^(3)+3(0.2)^(4)`

Using exponential rule:
`a^0=1`, so that
`0.2^0=1`

`=3(1)+0.6+0.12+0.024+0.0048`

`=3.7488`

= 3.75

`\sum_(n=1)^(5) 3(0.2)^(n-1)=3.75`

Option C is the correct answer.

Hence approximate value of
`\sum_(n=1)^(5) 3(0.2)^(n-1)` is 3.75.