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

Question

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 (A) - 12 (B) - 16 (C) - 18 (D) - 21

Tardigrade Admin · Accepted Answer

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 a1+a3+a5=-12 ∴ 3 a=-12 ⇒ a=-4 also a1 ⋅ a2 ⋅ a3=8 (a-2 d)(a-d) a=8 -4(-4-2 d)(-4-d)=8 ⇒ d=-3 Hence the A.P. is 2,-1,-4,-7,-10,-13, ldots ldots Hence a2+a4+a6=-21

Q. If for an A.P. a1​,a2​,a3​,…,an​,…. a1​+a3​+a5​=−12 and a1​a2​a3​=8 then the value of a2​+a4​+a6​ equals

- 12

- 16

- 18

- 21

Let the 1st 5 terms of the A.P. are seq SC a−2d,a−d,a,a+d,a+2d now a1​+a3​+a5​=−12 ∴3a=−12⇒a=−4 also a1​⋅a2​⋅a3​=8 (a−2d)(a−d)a=8 −4(−4−2d)(−4−d)=8⇒d=−3 Hence the A.P. is 2,−1,−4,−7,−10,−13,…… Hence a2​+a4​+a6​=−21

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