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If the first term of an infinite gp is 1 and every term equal the sum of the successive term. Find the common ratio of GP. Also find the fourth term

If the first term of an infinite gp is 1 and every term equal the sum of the successive term. Find the common ratio of GP. Also find the fourth term

Grade:10

1 Answers

Arun
25758 Points
4 years ago

t(n)=t(n+1)+t(n+2)+......=S(∞)-S(n)

ar^(n-1)=a/(1-r)-a{(1-r^n)/(1-r)}

r^(n-1){1-r}=1–1+r^n=r^n

r^(n-1)-r^n=r^n

r^(n-1)=2r^n

r^n/r=2r^n

1/r=2

r=½ 

 

Hence 4th term = a * r⁴ = 1 *(1/2)4 = 1/16

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