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

Find an explicitly-defined equation for the sequence with ${a}_{1}=4$, ${a}_{2}=8$, ${a}_{3}=12$
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amilazamiyn
${a}_{1}=4,{a}_{2}=8,{a}_{3}=12$
${a}_{2}-{a}_{1}=8-4=4$
${a}_{3}-{a}_{2}=12-8=4$
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.