# Find the sum to infinity of the following arithmetico - geometric sequence: 1,-43,79,-1027... - Mathematics and Statistics

Sum

Find the sum to infinity of the following arithmetico - geometric sequence:

1, -4/3, 7/9, -10/27 ...

#### Solution

The given sequence can be written as :

1 xx 1, 4 xx (-1/3), 7 xx (-1/3)^2, 10 xx (-1/3)^3, ...

This is arithmetico-geometric progression with

a = 1, d = 3, r = -1/3, where |r| = |-1/3| = 1/3 < 1

∴ sum to infinity of the A.G.P. is given by

S = "a"/(1 - "r") + "dr"/(1 - "r")^2

= 1/(1 - (-1/3)) + (3(-1/3))/[1 - (-1/3)]^2

= 1/((4/3)) - 1/((16/9))

= 3/4 - 9/16

= 3/16

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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 2 Sequences and Series
Exercise 2.5 | Q 2. (iii) | Page 38