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

Question

asked Aug 28, 2017 66.2k views

2 Answers

Metamagikum · Answer 1 · 2017-09-02T07:29:02+0000

Answer:

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
.

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