Question

PLEASE HELP!!!

Use the formula to evaluate the series 3 + 6 + 12 + 24 + 48 + 96

In the formula for a finite series a1 is the first term r is the common ratio and n is the number of terms.

A. 93

B. 192

C. 189

Answer 1

`3+6+12+24+48+96=3(1+2+4+8+16)=3(\underbrace{2^0+2^1+2^2+2^3+2^4}_(S_5))`

We have


`2S_5=2^1+2^2+2^3+2^4+2^5`

from which we find that


`S_5-2S_5=-S_5=2^0-2^5\implies S_5=2^5-1=31`

We want to find
`3S_5`, which has a value of
`3\cdot31=93`.

Answer 2

Sn = 189

Explanation:

From the series 3 + 6 + 12 + 24 + 48 + 96

First term a1: is the first term in the series

Common ratio (r) : is the ratio between the first term and the second, second term and the third term and so on. It can be gotten by dividing second term with first term or third term with the second and so on. It has to be common along the series.

n : is the number of terms

Therefore in this case.

First term a1 = 3

Common ratio r = 6/3 = 12/6 = 24/12 = 48/24 = 96/48 = 2

Common ratio r = 2

Number of terms n = 6

So,

Sn = a1(1-r^n)/(1-r)

Sn = 3(1 - 2^6) / (1 - 2)

Sn = 3(1 - 64) / (1 - 2)

Sn = 3(-63) / (-1)

Sn = -189 / -1

Sn = 189