Answer:
For a geometric sequence
[tex]a_1, a_2, a_3, a_4,..[/tex]
The nth term for this sequence is given by:
[tex]a_n = a_1r^{n-1}[/tex] .....[1]
where
[tex]a_1[/tex] is the first term
r is the common ratio
n is the number of terms.
Given the sequence:
80, -160, 320, -640
[tex]a_1 = 80[/tex]
[tex]a_2 = -160[/tex]
[tex]a_3 = 320[/tex]
[tex]a_4= -640[/tex]
Common ratio(r) is -2
Since,
[tex]r = \frac{a_2}{a_1}=\frac{a_3}{a_2}=\frac{a_4}{a_3}[/tex]
Substitute the values we have;
[tex]r = \frac{-160}{80}= \frac{320}{-160}=\frac{-640}{320} = -2[/tex]
We have to find the next three term of the given sequence:
Using [1] we have
[tex]a_5 = a_1 \cdot r^4[/tex]
Substitute the given values we have;
[tex]a_5 =80 \cdot (-2)^4 = 80 \cdot 16= 1280[/tex]
Similarly,
[tex]a_6 =80 \cdot (-2)^5= 80 \cdot -32=-2560[/tex]
[tex]a_7 =80 \cdot (-2)^6 = 80 \cdot 16 =5120[/tex]
Therefore, next three terms in the given sequence are: 1280, -2560, 5120
