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Many One Function

If for an A.P...

Question

If for an A.P. $a_{1}, a_{2}, a_{3} . . . . . . . . . a_{n},$ $a_{1} + a_{3} + a_{5} = - 12$ and $a_{1} a_{2} a_{3} = 8$ then the value of $a_{2} + a_{4} + a_{6}$ equals

A

- 12

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B

- 16

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C

- 18

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D

- 21

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Solution

The correct option is D $- 21$
Solution -
$A . P . \to a_{1}, a_{2}, . . . \dots . a_{n}$
First element $= a_{1}$
Common difference $=$ d
$a_{1} + a_{1} + 2 d + a_{1} + 4 d = - 12$
$3 a_{1} + 6 d = - 12$
$a_{1} + 2 d = - 4$ …… $(1)$
$a_{1} a_{2} a_{3} = 8$
$a_{1} (a_{1} + d) (a_{1} + 2 d) = 8$
Put $d_{1} = - 4 - 2 d$ from $(1)$
$(- 4 - 2 d) (- 4 - d) (- 4) = 8$
$(4 + 2 d) (4 + d) = - 2$
$16 + 4 d + 8 d + 2 d^{2} = - 2$
$2 d^{2} + 12 d + 18 = 0$
$d^{2} + 6 d + 9 = 0$
$(d + 3)^{2} = 0$
$d = - 3$
$a_{1} = - 4 + 6 = 2$
$a_{2} = a_{1} + d = - 1$
$a_{4} = a_{1} + 3 d = - 7$
$a_{6} = a_{1} + 5 d = - 13$
$a_{2} + a_{4} + a_{6} = (- 1) + (- 7) + (- 13) = - 21$
D is correct.

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Similar questions

A . P .

a_{1}, a_{2}, a_{3}, . . . . ., a_{n}, . . . ., a_{1} + a_{3} + a_{5} = - 12

a_{1} a_{2} a_{3} = 8

then the value of

a_{2} + a_{4} + a_{6}

A . P .

a_{1}, a_{2}, a_{3}, . . . . . ., a_{n}, . . . . .

a_{1} + a_{3} + a_{5} = - 12

a_{1} a_{2} a_{3} = 8

then the value of

a_{2} + a_{4} + a_{6}

\frac{3 x^{2} - 2 x + 4}{(x - 1)^{2}} = \frac{A_{1}}{x + 1} + \frac{A_{2}}{(x + 1)^{2}} + \frac{A_{3}}{(x + 1)^{3}} + \frac{A_{4}}{(x + 1)^{4}} + \frac{A_{5}}{(x + 1)^{5}} + \frac{A_{6}}{(x + 1)^{6}}

(A_{1} + A_{3} + A_{5}, A_{2} + A_{4} + A_{6}) =

a_{1}, a_{2}, a_{3}, a_{4}, a_{5}

are first five terms of an A.P. such that

a_{1} + a_{3} + a_{5} = - 12

a_{1} a_{2} a_{3} = 8

. Find the first term and the common difference.

Q. For an A.P.,

a_{1}, a_{2}, a_{3}, \dots \dots

a_{3} + a_{5} + a_{8} = 11

a_{4} + a_{2} = - 2

, then the value of

a_{1} + a_{6} + a_{7}

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