Answer:
The general rule for the nth term of this sequence will be:
[tex]a_n=3na+9a[/tex]
Step-by-step explanation:
Given the sequence
12a, 15a, 18a, 21a, 24a,...
An arithmetic sequence has a constant difference 'd' and is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
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
[tex]a_n=a_1+\left(n-1\right)d[/tex]
substituting a₁ = 12a, d = 3a
[tex]a_n=12a+\left(n-1\right)3a[/tex]
[tex]=12a+3na-3a[/tex]
[tex]=3na+9a[/tex]
Therefore, the general rule for the nth term of this sequence will be:
[tex]a_n=3na+9a[/tex]
