11TH•Mathematics•Sequences And Series•6.8 Arithmetico-Geometric Progression

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

A.G.P. sequences and series, finite and infinite sums.

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If $\{a_n\}$ is an A.P. and $\{b_n\}$ is a G.P., then $\{a_n b_n\}$ is an arithmetico-geometric sequence.

With A.P. $a, a+d, \ldots$ and G.P. $b, br, \ldots$ ( $r \neq 1$ ):

ab,\ (a+d)br,\ (a+2d)br^2,\ \ldots,\ \bigl[a+(n-1)d\bigr]br^{n-1}

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