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nth Term of A.P

For what valu...

Question

For what value of $k$ , are $k - 3, 2 k + 1$ and $4 k + 3$ are in $A . P$ .?

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Solution

common difference must be same between the successive terms for a series to be in ap
$(2 k + 1) - (k - 3) = (4 k + 3) - (2 k + 1)$
$k + 4 = 2 k + 2$
$k = 2$

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