Question

I need help finding this sigma-notation sum. I'm not quite sure what to do with the exponent, I have determined a1 = 12, a2=36, a3=108, and a4=324. I notice the pattern of multiplying by 3 each segment, but I'm struggling how to equate this to a form that is simple enough to call an answer.$3^{k}$

Answer 1

I have added a₀ to reach the logic of your formula (and a₀ responds perfectly to the pattern 

a₀ = 4 =  4 x 1 = 4 x 3⁰

a₁ = 12 = 4x3 = 4 x 3¹

a₂ = 36 = 4 x 9 = 4 x 3²

a₃ =108 = 4 x 27 = 4 x 3³

a₄ = 324 = 4 x 81 = 4 x 3⁴

a(n) ==========4 x 3ⁿ

ⁿ
Σ 4 x 3^(k-1)
k=1