Question

Find the next three terms of the sequence  80, –160, 320, –640

Answer 1

You times by -2 1280 -2560 5120

Answer 2

For a geometric sequence

`a_1, a_2, a_3, a_4,..`

The nth term for this sequence is given by:

`a_n = a_1r^(n-1)` .....[1]

where

`a_1` is the first term

r is the common ratio

n is the number of terms.

Given the sequence:

80, -160, 320, -640

`a_1 = 80`

`a_2 = -160`

`a_3 = 320`

`a_4= -640`

Common ratio(r) is -2

Since,

`r = (a_2)/(a_1)=(a_3)/(a_2)=(a_4)/(a_3)`

Substitute the values we have;

`r = (-160)/(80)= (320)/(-160)=(-640)/(320) = -2`

We have to find the next three term of the given sequence:

Using [1] we have

`a_5 = a_1 \cdot r^4`

Substitute the given values we have;

`a_5 =80 \cdot (-2)^4 = 80 \cdot 16= 1280`

Similarly,

`a_6 =80 \cdot (-2)^5= 80 \cdot -32=-2560`

`a_7 =80 \cdot (-2)^6 = 80 \cdot 16 =5120`

Therefore, next three terms in the given sequence are: 1280, -2560, 5120