Question

Which function can be used to determine the nth term of the sequence?

Answer 1

Option (C)

Explanation:

Recursive formula of sequence is,

`a_1=-7`

`a_n=a_(n-1)-5`

Therefore, sequence will be in the form of,

-7, -12, -17,......

Therefore, common difference of the given arithmetic sequence,

d =
`a_n-a_(n-1)`

= -5

Explicit formula for an arithmetic sequence is,

f(n) = a + (n - 1)d

where a = first term of the sequence

n = nth term

d = common difference in each successive term

By substituting the values from the sequence,

f(n) = -7 + (n - 1)(-5)

= - 7 - 5(n - 1)

= -7 - 5n + 5

f(n) = -5n - 2

Option (C) will be the correct option.