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Find S(oo) of the G.P. whose first term ...

Find `S_(oo)` of the G.P. whose first term is 28 and the fourth term is `(4)/(49)` .

Text Solution

Verified by Experts

Let r be the common ratio of the G.P.
Given a = first term = 28
and ` a_(4) = ar^(3) = (4)/(49)`
`therefore r^(3) = (4)/((49)/(28)) = (1)/(343)`
`rArr r = (1)/(7)`
Clearly `|r| lt 1 `
` therefore ` Sum to infinity of the G.P.
`S_(oo) = (a)/(1-r) = (28)/(1-(1)/(7)) = 28 xx (7)/(6)`
`= (98)/(3)`
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