If a 1- a 2- a 3- are in A-P- then a p - a q - a r are in A-P if p - q - r are inA- H-PB- A-PC- G-PD- None of these

The correct option is B A.P a_p, a_q, a_r are in A.P ⇒ a_p + a_r = 2a_q Let d be the common difference a_1+(p 1)d+(a_1+(r 1)d=2(a_1+(q 1)d 2a_1+(p+r)d 2d=2a_1+ ...

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Byju's Answer

Standard XII

Mathematics

Focus

If a 1, a 2, ...

Question

If $a_{1}, a_{2}, a_{3} . . .$ are in A.P, then $a_{p}, a_{q}, a_{r}$ are in A.P if p, q, r are in

A.P

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G.P

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H.P

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None of these

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Solution

The correct option is A
A.P

$a_{p}, a_{q}, a_{r}$ are in A.P
$\Rightarrow a_{p} + a_{r} = 2 a_{q}$
Let d be the common difference
$a_{1} + (p - 1) d + (a_{1} + (r - 1) d = 2 (a_{1} + (q - 1) d$
$2 a_{1} + (p + r) d - 2 d = 2 a_{1} + 2 q d - 2 d$
$\Rightarrow$ p+r=2q
$\Rightarrow$ p,q,r are in A.P

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