Arithmetic: (3,7,11,\ldots) → (a_n=3+(n-1)4=4n-1)
Geometric: (2,6,18,\ldots) → (b_n=2\cdot 3^{n-1})
[ t_n = (4n-1)\cdot 2\cdot 3^{n-1} = 2(4n-1)3^{n-1} ]
Answer: (t_n=2(4n-1)3^{n-1})
11TH•Mathematics•Sequences And Series•Question 2
Overview
Find the $n^{th}$ term of the arithmetico-geometric sequence, where the arithmetic part is $3, 7, 11, \ldots$ and the geometric part is $2, 6, 18, \ldots$.
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