Question

Write down an expression for the nth term of the following sequence

7, 11, 15, 19, ...

Answer 1

`a_(n)` = 4n + 3

Explanation:

There is a common difference d between consecutive terms , that is

d = 11 - 7 = 15 - 11 = 19 - 15 = 4

This indicates the sequence is arithmetic with n th term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 7 and d = 4 , then

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