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how to solve arithmetico geometric progression

how to solve arithmetico geometric progression

Grade:11

1 Answers

Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
9 years ago

Suppose a1, a2, a3......is an A.P. and b1, b2, b3..... is a G.P. Then the Progression a1b1, a2b2, ....... is said to be an arithmetico-geometric progression (A.G.P). Hence an arithmetico-geometric progression is of the form ab, (a+d)br, (a+2d)br2, (a+3d)br3,.........

Sum of n Terms

The sum Snoffirstntermsof anA.G. P.isobtained inthe followingway :

Sn= ab + (a + d)br + (a + 2d)br2+.........+(a + (n - 2)d)brn-2+ (a + (n - 1)d)brn-1

Multiply both sides by r, so that

r Sn= abr + (a + d)br2+.........+(a + (n - 3)d)brn-2+ (a + (n - 2)d)brn-1+ (a + (n - 1)d)brn

Subtracting, we get

(1 - r)Sn= ab + dbr + dbr2+.......+dbrn - 2+ dbrn - 1- (a + (n - 1)d)brn

=ab + dbr/(1–rn–1)/(1–r) – (a+(n–1)d)brn=> Sn= ab/1–r + dbr(1–rn–1)/(1–r)2– (a+(n–1)d)brn/1–r

If -1 < r < 1, the sum of the infinite number of terms of the progression is

= .

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