Question

Find an explicit formula for the arithmetic sequence -45,-30,-15

Answer 1

`a_(n)` = 15n - 60

Explanation:

the nth term ( explicit formula) for an arithmetic sequence is

`a_(n)` = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = - 45 and d = a₂ - a₁ = - 30 - (- 45) = - 30 + 45 = 15

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