Question

Which functions represent the arithmetic sequence 8, 1.5, –5, –11.5 . . . ? Check all that apply. f(n) = –6.5n + 14.5 f(n) = –1.5n + 9.5 f(n) = 6.5n + 1.5 f(1) = 8, f(n + 1) = f(n) – 6.5 f(1) = 8, f(n + 1) = f(n) – 1.5 f(1) = 8, f(n + 1) = f(n) + 6.5

Answer 1

f(n) = –6.5n + 14.5

f(1) = 8, f(n + 1) = f(n) – 6.5

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Answer 2

If you would like to know which functions represent the arithmetic sequence 8, 1.5, -5, -11.5, ... you can find this using the following steps:

f(n) = –6.5n + 14.5 ... yes
f(1) = 8
f(2) = 1.5
f(3) = -5
f(4) = -11.5

f(n) = –1.5n + 9.5 ... no
f(1) = 8
f(2) = 6.5

f(n) = 6.5n + 1.5 ... no
f(1) = 8
f(2) = 14.5

f(1) = 8, f(n + 1) = f(n) – 6.5 ... yes
f(2) = 8 - 6.5 = 1.5
f(3) = 1.5 - 6.5 = -5
f(4) = -5 - 6.5 = -11.5

f(1) = 8, f(n + 1) = f(n) – 1.5 ... no
f(2) = 8 - 1.5 = 6.5

f(1) = 8, f(n + 1) = f(n) + 6.5 ... no
f(2) = 8 + 6.5 = 14.5

The correct result would be:
f(n) = –6.5n + 14.5 and f(1) = 8, f(n + 1) = f(n) – 6.5.