Question

Evaluate the summation of 20 times 0.5 to the n minus 1 power, from n equals 3 to 12.

Answer 1

Answer: 9.99

Explanation:

I just took the quiz!

Answer 2

The sum of the series is 9.99

Explanation:

We are given the series
`\sum_(n=3)^(12)20(0.5)^(n-1)`.

So,
`a_(n)=20(0.5)^(n-1)`, where n=3 to 12

Then, we have,

`1.\ a_(3)=20(0.5)^(3-1)\\a_(3)=20(0.5)^(2)\\a_(3)=5`

`2.\ a_(4)=20(0.5)^(4-1)\\a_(4)=20(0.5)^(3)\\a_(4)=2.5`

Thus, the common ratio is
`r=(2.5)/(5)=0.5`

Since, the sum of first n terms of a series is
`S=(a_(1)(1-r^(n)))/(1-r)`.

As n = 3 to 12, then the number of terms = 10, first term=a₃= 5 and r= 0.5

So, the sum of 10 terms is
`S=(5(1-(0.5)^(10)))/(1-0.5)`

i.e.
`S=(5(1-0.00098))/(0.5)`

i.e.
`S=(5* 0.99902)/(0.5)`

i.e.
`S=(4.9951)/(0.5)`

i.e. S = 9.99

Hence, the sum of the series is 9.99