Question no 28

Question no 28 20. of in is •G

Dear Student,

Let the first term be a and common difference as d, hence the terms in the AP will be;

a, a+d, a+2d, a+3d.....

Where, nth term Tn=a+(n-1)d
since, a1+a3+a5=-12or, a+a+2d+a+4d=-12         as a3=a+2d, a5=a+4d by nth term formulaor, 3a+6d=-12or, a+2d=-4.....(i)Now, as a1a2a3=8or, a(a+d)(a+2d)=8or, a(a+d)(-4)=8            from (i) as a+2d=-4or, a2+ad=-2Putting the value of d from (i), we get a2+a(-4-a2)=-2or, 2a2+a(-4-a)=-2×2or, 2a2-4a-a2=-4or, a2-4a+4=0or, a-22=0or, a=2Putting the value of a in equation (i), we get,2+2d=-4or, 2d=-6or, d=-3

Hence, 

=a2+a4+a6=a+d+a+3d+a+5d=3a+9d=3(2)+9(-3)=6-27=-21

Hope this information will clear your doubts about the topic.

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