Question

Here are the first 5 terms in a number sequence 7 10 13 16 19

write an expresstion, in terms of n, for the nth term of this number sequence.

Answer 1

`a_(n)` = 3n + 4

Explanation:

there is a common difference between consecutive terms , that is

10 - 7 = 13 - 10 = 16 - 13 = 19 - 16 = 3

this indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 7 and d = 3 , then

`a_(n)` = 7 + 3(n - 1) = 7 + 3n - 3 = 3n + 4