Question

The first term of a geometric sequence is 4 and the multiplier, or ratio, is –2. What is the sum of the first 5 terms of the sequence?

Answer 1

`S_5=44`

Explanation:

`"the sum to n terms of a geometric sequence is"`

`•color(white)(x)S_n=(a(r^n-1))/(r-1)`

`"where a is the first term and r the common ratio"`

`"here "a=4" and "r=-2`

`S_5=(4((-2)^5-1))/(-2-1)`

`color(white)(S_5)=(4(-32-1))/(-3)=(-132)/(-3)=44`

`"Alternatively"`

`"listing the first five terms of the sequence"`

`4,-8,16,-32,64`

`S_5=4-8+16-32+64=44`

Answer 2

`=S_5=44`

Explanation:

The sum of first `n` term of geometric sequence is :

`color(blue)(S_n=(a_1(1-r^n))/(1-r)`

Where , `a_1=` first term `and r=` common ratio.

We have , `a_1=4 and r=(-2)`

So, the sum of first `5` terms is`=S_5ton=5`

`:.S_5=(4(1-(-2)^5))/(1-(-2))`

`=>S_5=(4(1-(-32)))/(1+2)`

`=>S_5=(4(1+32))/3=(4xx33)/3=4xx11`

`=>S_5=44`