The first term of an A.P is same as that of G.P .the common difference of one and the common ration of other are both 4.if the sum of the first three terms of both series are same ,find the fourteenth terms of each series?

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Answer 1 · 2017-09-14T14:32:55

Let the first term of an A.P and that of G.P be #a#

Given that the common difference of one and the common ration of other are both 4.

if the sum of the first three terms of both series are same then

#a+(a+4)+(a+8)=a+4a+16a#

#=>18a=12#

#=>a=2/3#

So the fourteenth term of AP is #=2/3+(14-1)xx4=52 2/3#

And the fourteenth term of GP is #=2/3xx4^(14-1)==2/3xx4^13#