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  4. If for an A.P. a1, a2, a3, ldots, an, ldots. a1+a3+a5=-12 and a1 a2 a3=8 then the value of a2+a4+a6 equals

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Q. If for an A.P. $a_1, a_2, a_3, \ldots, a_n, \ldots$. $a_1+a_3+a_5=-12$ and $a_1 a_2 a_3=8$ then the value of $a_2+a_4+a_6$ equals

Sequences and Series

Solution:

Let the $1^{\text {st }} 5$ terms of the A.P. are
$seq$ SC
$a-2 d, a-d, a, a+d, a+2 d$
now $a_1+a_3+a_5=-12$
$\therefore \quad 3 a=-12 \quad \Rightarrow \quad a=-4$
also $a_1 \cdot a_2 \cdot a_3=8$
$(a-2 d)(a-d) a=8 $
$-4(-4-2 d)(-4-d)=8 \Rightarrow d=-3$
Hence the A.P. is $2,-1,-4,-7,-10,-13, \ldots \ldots$
Hence $a_2+a_4+a_6=-21$