Question

What expression shows the relationship between the value of any term and n, its position in the sequence for the given sequence?

10, 5, 0, -5, -10, ...
A) -5n
B) -5n + 15
C) -3n + 15
D) 5n

Answer 1

B

Explanation:

These are the terms of an arithmetic sequence with n th term

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

where d is the common difference and
`a_(1)` the first term

here d = - 10 - (- 5) = - 5 - 0 = 0 - 5 = - 5 and
`a_(1)` = 10, hence

`a_(n)` = 10 - 5(n - 1) = 10 - 5n + 5 = 15 - 5n → B