Question

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

a. = 3mn + 9m
b. = -3mn - 9m
c. = -3mn + 9m
d. = 3mn - 9m

Answer 1

The given sequence is
12m, 15m, 18m, 21m, 24m, ...,

The 1st term is a₁ = 12m
The 2nd term is a₂ = 15m = a₁ + 3m = a₁ + (2-1)*3m
The 3rd term is a₃ = 18m = a₂ + 3m = a₁ + (3-1)*3m

Because each successive term is 3m more than the previous term, we have an arithmetic sequence with a common difference of 3.

Answer:
The n-th term is

`a_(n) = a_(1) + (n-1)*(3m),\\for\, n=1,2,3,\,...,`

In recursive form,

`a_(n+1)=a_(n)+3m`