What is an Arithmetic Geometric Progression?
An Arithmetic Geometric Progression or simply AGP, is basically a combination of an Arithmetic Progression and a Geometric Progression as name indicates. Mathematically, an AGP is obtained by taking the product of each term of an AP with the corresponding term of a GP. That is, an AGP is of the form a1b1, a2b2, a3b3,... where a1, a2, a3,... is an AP and b1, b2, b3,... is a GP. If d is the common difference and a is the first term of the AP, and r is the common ratio of the GP then the nth term of the AGP will be (a + (n-1)d)(r^(n-1)).
How to Calculate Sum of First N Terms of Arithmetic Geometric Progression?
Sum of First N Terms of Arithmetic Geometric Progression calculator uses Sum of First N Terms of Progression = ((First Term of Progression-((First Term of Progression+(Index N of Progression-1)*Common Difference of Progression)*Common Ratio of Progression^(Index N of Progression)))/(1-Common Ratio of Progression))+(Common Difference of Progression*Common Ratio of Progression*(1-Common Ratio of Progression^(Index N of Progression-1))/(1-Common Ratio of Progression)^2) to calculate the Sum of First N Terms of Progression, The Sum of First N Terms of Arithmetic Geometric Progression formula is defined as the summation of the terms starting from the first to the nth term of given Arithmetic Geometric Progression. Sum of First N Terms of Progression is denoted by Sn symbol.
How to calculate Sum of First N Terms of Arithmetic Geometric Progression using this online calculator? To use this online calculator for Sum of First N Terms of Arithmetic Geometric Progression, enter First Term of Progression (a), Index N of Progression (n), Common Difference of Progression (d) & Common Ratio of Progression (r) and hit the calculate button. Here is how the Sum of First N Terms of Arithmetic Geometric Progression calculation can be explained with given input values -> 1221 = ((3-((3+(6-1)*4)*2^(6)))/(1-2))+(4*2*(1-2^(6-1))/(1-2)^2).