Question

Find an equation for the nth term of the arithmetic sequence.
-20, -16, -12, -8, ...

Answer 1

The difference each time is 4 so first we must do 4n which in a sequence equals 4, 8, 12... but the actually sequence is -20, -16, -12... so to turn 4 into - 20 we have to -24 and the same goes for 8 into -16 and 12 into -12. Thus meaning the nth term is 4n - 24.

Answer 2

The equation for a arithmetic sequence is an=a1+d(n-1)

The answer would be -20+4(n-1) since the first term (a1) is -20. The difference (d) is +4 each time. We use (n-1) in order to find the answer without the previous term (arithmetic sequence).

Proving this equation:

a1=-20+4(1-1)=-20

a2=-20+4(2-1)=-20+4=-16

a3=-20+4(3-1)=-20+8=-12

a4=-20+4(4-1)=-20+12=-8

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