Question

Indicate a general rule for the nh term of this sequence.
12a, 15a, 18a, 21a, 24a,...

Answer 1

The general rule for the nth term of this sequence will be:

`a_n=3na+9a`

Explanation:

Given the sequence

12a, 15a, 18a, 21a, 24a,...

An arithmetic sequence has a constant difference 'd' and is defined by

`a_n=a_1+\left(n-1\right)d`

Here,

a₁ = 12a

computing the differences of all the adjacent terms

d = 15a-12a = 3a, d = 18a-15a=3a, d=21a-18a=3a, d=24a-21a=3a

using the nth term formula

`a_n=a_1+\left(n-1\right)d`

substituting a₁ = 12a, d = 3a

`a_n=12a+\left(n-1\right)3a`

`=12a+3na-3a`

`=3na+9a`

Therefore, the general rule for the nth term of this sequence will be:

`a_n=3na+9a`