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(n) = 8, f(n+1) = f(n) -6.5

The first is the explicit definition, the other one is the corresponding recursive definition. In this sequence we can note that the first term f(1) is 8, the f(0) term is 14.5, and the difference d= -6.5.

Answer 2

f(n) = –6.5n + 14.5

f(1) = 8, f(n + 1) = f(n) – 6.5

Explanation:

The nth term of an arithmetic sequence is given as

Tn = a + (n-1)d

where a is the first term and d is the common difference between two consecutive terms

From the given sequence,

a = 8, d = 1.5 - 8

d = -6.5

As such, Tn = f(n) = 8 + (n-1)-6.5

= 8 - 6.5n + 6.5

= 14.5 - 6.5n

f(1) = 8

f(n + 1) - f(n) = – 6.5

f(n + 1) = f(n) – 6.5