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

Sagot :

You times by -2 1280 -2560 5120

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