Theory of Intelligence
11TH•Mathematics•Sequences And Series•Exercise 6.8

6.8 Arithmetico-Geometric Progression (A.G.P.)

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Question 1

Find the 8th term of the arithmetico-geometric sequence, where the arithmetic part is 1,4,7,…1, 4, 7, \ldots and the geometric part is 5,10,20,…5, 10, 20, \ldots.

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Step-by-Step Solution

Question 1

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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)

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