Question

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

Answer 1

170.5 is the answer from the TI-84

Answer 2

Answer:

The sum of the given geometric series is:

                             170.5

Step-by-step 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 :

$S_n=a\times (\dfrac{r^n-1}{r-1})$

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:

$S_5=\dfrac{1}{2}\times (\dfrac{4^5-1}{4-1})\\\\\\S_5=\dfrac{1}{2}\times (\dfrac{1023}{3})\\\\\\S_5=170.5$

Hence, the sum of the series is: 170.5