Question

Write an explicit formula for an, the nth term of the sequence 25,30,35,....

Answer 1

`a_(n)` = 5n + 20

Explanation:

there is a common difference between consecutive terms in the sequence

30 - 25 = 35 - 30 = 5

this indicates the sequence is arithmetic with explicit formula

`a_(n)` = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 25 and d = 5 , then

`a_(n)` = 25 + 5(n - 1) = 25 + 5n - 5 = 5n + 20