Arithmetic part: (1,4,7,\ldots) → (a_n=1+(n-1)3=3n-2)
Geometric part: (5,10,20,\ldots) → (b_n=5\cdot 2^{n-1})
8th term of A.G. sequence: [ t_8 = a_8\cdot b_8 = (3\cdot8-2)\cdot 5\cdot 2^{7} = 22\cdot 5\cdot 128 = 14080 ]
Answer: (14080)
11TH•Mathematics•Sequences And Series•Question 1
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Find the 8th term of the arithmetico-geometric sequence, where the arithmetic part is $1, 4, 7, \ldots$ and the geometric part is $5, 10, 20, \ldots$.
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