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If for an AP A1,A2,A3....an. A1+A3+A5=-12 and A1*A2*A3=8. Find the value of A2+A4+A6.

If for an AP A1,A2,A3....an. A1+A3+A5=-12 and A1*A2*A3=8. Find the value of A2+A4+A6.

Grade:11

2 Answers

Ajay
209 Points
7 years ago
Let d be the common difference .
A1+ (A1+2d) + (A1+4d) = -12 and
A1*(A1+2d) *(A1+4d) =  8  and
solve equations for A1 and d 
Now A2+A4+A6 = (A1+d) + (A1+3d) + (A1+5d).
Substitute values for A1 and d found in previous step.
Ajay
209 Points
7 years ago
Shorter method
 
Let d be the common difference .
(A3-2d)+ A3 + (A3+2d) = -12 and
A3 = -4
(A3-2d)* (A3-d) *(A3) =  8 
Solve for d 
Now A2+A4+A6 = (A3-d) + (A3+d) + (A3+2d).
Substitute values for A3 and d found in previous step.

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