Question

What is an explicitly-defined equation for the sequence with `a_1`=4, `a_2`=8, `a_3=12`?

Answer 1

nth term `a_n = 4 + (n-1) * 4` is the explicitly defined equation of the giver Arithmetic Sequence.

Explanation:

`a_1 = 4, a_2 = 8, a_3 = 12`

`a_2 - a_1 = 8 - 4 = 4`

`a_3 - a_2 = 12 - 8 = 4`

Hence common difference `d = 4`

It is an Arithmetic Sequence with `a_1 = 4, d = 4`

nth term of A.S. is given by `a_n = a_1 + (n-1) * d` where n is a positive integer.

nth term `a_n = 4 + (n-1) * 4` is the explicitly defined equation of the giver Arithmetic Sequence.