Question

Use the geometric series equation to answer each question.

What are the terms in the series?

1 + 8 + ____ + ____ + ____

Answer 1

Answer: 1 + 8 + 64 + 512 + 4096

the third partial sum is 73

Answer 2

64, 512, 4096 respectively.

Explanation:

The given geometric series is

`\sum\limits_(n=1)^5(8)^(n-1)`

It can be rewritten as

`\sum\limits_(n=1)^5(8)^(n-1)=(8)^(1-1)+(8)^(2-1)+(8)^(3-1)+(8)^(4-1)+(8)^(5-1)`

`\sum\limits_(n=1)^5(8)^(n-1)=(8)^(0)+(8)^(1)+(8)^(2)+(8)^(3)+(8)^(4)`

`\sum\limits_(n=1)^5(8)^(n-1)=1+8+64+512+4096` ...(i)

It is given that the series is defined as

`1 + 8 +\underline{\quad } +\underline{\quad }+\underline{\quad }` ...(ii)

From (i) and (ii), it is clear that the missing values are 64, 512, 4096 respectively.