Question

The first five terms of a sequence are a1=47, a2=33, a3=19, a4=5, a5=−9


Based on this information, create an equation that can be used to find the nth term of the sequence, an
.

Choose from the list of numbers below to fill in the blanks. Not all answers will be used.

61
47
-14
-61
14

an = ___n+___

Answer 1

Differences are constant: 33−47 = −14, etc., so d = −14. Using a1 = 47:
an = 47 + (n−1)(−14) = 61 − 14n.
Thus an = −14n + 61.