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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
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^nr^(n-1)-r^n=r^nr^(n-1)=2r^nr^n/r=2r^n1/r=2r=½ Hence 4th term = a * r⁴ = 1 *(1/2)4 = 1/16
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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