Question

for what value of p, are 2 p + 1, 13, 5 - 3p three consecutive terms of an ap

Answer 1

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If these 3 given terms are consecutive, then the $<b>difference between</b>$ any 2 terms will also be same.

•°•

$\sf{a_2 - a = a_3 - a_2}$

13 - ( 2p + 1 ) = 5 - 3p - ( 13 )

13 - 2p - 1 = 5 - 3p - 13

- 2p + 3p = 5 + 1 - 13 - 13

p = 6 - 26

$<b>p = - 20</b>$

Answer 2

$\large\mathfrak{\underline{\underline{Solution :}}}$

$\text{If the given 3 terms are consecutive,}$
$\text{then the difference between terms will}$
$\text{be same.}$

$\sf{a = 2p + 1}$

$\sf{a_2 = 13}$

$\sf{a_3 = 5 - 3p}$

$\therefore$

$\sf{\implies a_2 - a = a_3 - a_2}$

$\sf{\implies 13 - (2p + 1) = 5 - 3p - (13)}$

$\sf{\implies 13 - 2p - 1 = 5 - 3p - 13}$

$\sf{\implies - 2p + 3p = 5 + 1 - 13 - 13}$

$\sf{\implies p = 6 - 26}$

$\sf\red{\implies p = - 20}$