What is the summation notation for the geometric sequence 1/2+2+8+32+128

Question

asked Sep 7, 2018 104k views

2 Answers

MacGile · Answer 1 · 2018-09-12T18:26:57+0000

Answer:

The sum of the given geometric series is:

170.5

Explanation:

We know that for any geometric series have 'n' terms with first terms as: ''a'' and common ratio of the terms in the series as: 'r'

We get the sum of the series by the formula :

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

From the question we have:

a=1/2 , r=4 ( Since each term is the series is 4 times it's preceding term) and n=5 (as there are five terms in the series )

Hence, the sum of the series is:

$S_5=(1)/(2)* ((4^5-1)/(4-1))\\\\\\S_5=(1)/(2)* ((1023)/(3))\\\\\\S_5=170.5$

Hence, the sum of the series is: 170.5