Question

Find an explicit formula for the arithmetic sequence -45,-30,-15,0,...−45,−30,−15,0,...minus, 45, comma, minus, 30, comma, minus, 15, comma, 0, comma, point, point, point.

c(n)=c(n)=c, left parenthesis, n, right parenthesis, equals

Answer 1

`a_(n)` = 15n - 60

Explanation:

The n th term ( explicit formula ) of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 45 and d = - 30 - (- 45) = - 30 + 45 = 15, thus

`a_(n)` = - 45 + 15(n - 1) = - 45 + 15n - 15 = 15n - 60