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Common Difference

For what valu...

Question

For what value of $K K + 9, 2 K - 12 K + 7$ are consecutive terms of ap

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Solution

Here,
$a_{1} = K + 9$
$a_{2} = 2 K - 1$
$a_{3} = 2 K + 7$
Common difference is $d$ .
If they are in $A P$ then $d$ will be same throughout.
$∴$ $a_{2} - a_{1} = a_{3} - a_{2}$
$\Rightarrow$ $(2 K - 1) - (K + 9) = (2 K + 7) - (2 K - 1)$
$\Rightarrow$ $2 K - 1 - K - 9 = 2 K + 7 - 2 K + 1$
$\Rightarrow$ $K - 10 = 8$
$∴$ $K = 18$
$∴$ Value of $K$ is $18$ .

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