Question

Write an explicit formula for an, the nth term of the sequence 25,33,41

Answer 1

`a_(n)` = 8n + 17

Explanation:

there is a common difference between consecutive terms in the sequence

33 - 25 = 41 - 33 = 8

this indicates the sequence is arithmetic with explicit formula

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 25 and d = 8 , then explicit formula is

`a_(n)` = 25 + 8(n - 1) = 25 + 8n - 8 = 8n + 17