If an be the nth term of an AP and if a7=15, then the value of the common difference that would make a2a7a12 greatest is

Question

If an be the nth term of an AP and if a7=15, then the value of the common difference that would make a2a7a12 greatest is (A) 9 (B) 9/4 (C) 0 (D) 18

Tardigrade Admin · Accepted Answer

Let d be the common difference of AP. Since, a7=15 ∴ a2=15-5d and a12=15+5d Now, a2a7a12=(15-5d)(15)(15+5d) =15.25(3-d)(3+d) =375(9-d2) Clearly, this will be greatest, if d=0

Q. If $a_{n}$ be the nth term of an AP and if $a_{7} = 15,$ then the value of the common difference that would make $a_{2} a_{7} a_{12}$ greatest is

9

9/4

0

18

Let d be the common difference of AP. Since, $a_{7} = 15$ $∴$ $a_{2} = 15 - 5 d$ and $a_{12} = 15 + 5 d$ Now, $a_{2} a_{7} a_{12} = (15 - 5 d) (15) (15 + 5 d)$ $= 15.25 (3 - d) (3 + d)$ $= 375 (9 - d^{2})$ Clearly, this will be greatest, if $d = 0$

Q. If an​ be the nth term of an AP and if a7​=15, then the value of the common difference that would make a2​a7​a12​ greatest is

9

9/4

0

18

Let d be the common difference of AP. Since, a7​=15 ∴ a2​=15−5d and a12​=15+5d Now, a2​a7​a12​=(15−5d)(15)(15+5d) =15.25(3−d)(3+d) =375(9−d2) Clearly, this will be greatest, if d=0

Q. If $a_{n}$ be the nth term of an AP and if $a_{7} = 15,$ then the value of the common difference that would make $a_{2} a_{7} a_{12}$ greatest is

Let d be the common difference of AP. Since, $a_{7} = 15$ $∴$ $a_{2} = 15 - 5 d$ and $a_{12} = 15 + 5 d$ Now, $a_{2} a_{7} a_{12} = (15 - 5 d) (15) (15 + 5 d)$ $= 15.25 (3 - d) (3 + d)$ $= 375 (9 - d^{2})$ Clearly, this will be greatest, if $d = 0$