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

Mar 17, 2018

nth term ${a}_{n} = 4 + \left(n - 1\right) \cdot 4$ 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 ${a}_{n} = {a}_{1} + \left(n - 1\right) \cdot d$ where n is a positive integer.

nth term ${a}_{n} = 4 + \left(n - 1\right) \cdot 4$ is the explicitly defined equation of the giver Arithmetic Sequence.