Question

is AGP a common type of sequences

Answer 1

Answer:

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Arithmetic-Geometric Progression

An arithmetic-geometric progression (AGP) is a progression in which each term can be represented as the product of the terms of an arithmetic progressions (AP) and a geometric progressions (GP).

In the following series, the numerators are in AP and the denominators are in GP:

\large \dfrac{\color{#3D99F6}{1}}{\color{#D61F06}{2}}+\dfrac{\color{#3D99F6}{2}}{\color{#D61F06}{4}}+\dfrac{\color{#3D99F6}{3}}{\color{#D61F06}{8}}+\dfrac{\color{#3D99F6}{4}}{\color{#D61F06}{16}}+\dfrac{\color{#3D99F6}{5}}{\color{#D61F06}{32}}+\cdots= \, ?

2

1

+

4

2

+

8

3

+

16

4

+

32

5

+⋯=?

Arithmetic-geometric progressions are nice to work with because their sums can be evaluated easily, and this tool is used in a variety of contest problems.

Answer 2

Input : First term of AP, a = 1,

Common difference of AP, d = 1,

First term of GP, b = 2,

Common ratio of GP r = 2,

Number of terms, n = 3

Output : 34

Explanation

Sum = 1*2 + 2*22 + 3*23

= 2 + 8 + 24

= 34

So , yes AGP is a common type of sequences