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("io) Determine the number of terms in a...

("io) Determine the number of terms in a G.P.if "a_(1)=3,a_(n)=96" and "S_(n)=

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A sequence is called an A.P. if the difference of a term and the previous term is always same i.e. if a_(n+1)-a_(n) = constant (common difference) for all n in N . For an A.P. whose first term is 'a' and common difference is 'd' has its n^("th") term as t_(n)=a+(n-1)d Sum of n terms of an A.P. whose first is a, last term is I and common difference is d is S_(n)=(n)/(2)(2a+(n-1)d) =(n)/(2)(a+a+(n-1)d)=(n)/(2)(a+l) . If a_(1),a_(2),............,a_(n) are in G.P. then log_(a_(1))a,log_(a_(2))a,log_(a_(3))a,...log_(a_(n)) a are in