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

You times by -2 1280 -2560 5120

Answered by jayjayjay | 2024-06-10

For a geometric sequence
a 1 ​ , a 2 ​ , a 3 ​ , a 4 ​ , ..
The nth term for this sequence is given by:
a n ​ = a 1 ​ r 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 1 ​ a 2 ​ ​ = a 2 ​ a 3 ​ ​ = a 3 ​ a 4 ​ ​
Substitute the values we have;
r = 80 − 160 ​ = − 160 320 ​ = 320 − 640 ​ = − 2
We have to find the next three term of the given sequence:
Using [1] we have
a 5 ​ = a 1 ​ ⋅ r 4
Substitute the given values we have;
a 5 ​ = 80 ⋅ ( − 2 ) 4 = 80 ⋅ 16 = 1280
Similarly,
a 6 ​ = 80 ⋅ ( − 2 ) 5 = 80 ⋅ − 32 = − 2560
a 7 ​ = 80 ⋅ ( − 2 ) 6 = 80 ⋅ 16 = 5120
Therefore, next three terms in the given sequence are: 1280, -2560, 5120 ;

Answered by OrethaWilkison | 2024-06-12

The next three terms of the sequence 80, -160, 320, -640 are 1280, -2560, and 5120. This is determined by identifying the common ratio of -2. We use the formula for the nth term of the geometric sequence to calculate these terms.
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Answered by OrethaWilkison | 2024-12-18