Question

If $2k+1,13$ and $5k-3$ are three consecutive terms in an A.P., then, $k=$

• A. $17$
• B. $13$
• C. $4$
• D. $9$

Answer 1

The correct option is C $4$

$2k+1,13$ and $5k-3$ are three consecutive terms of an A.P

Then, difference of first two terms is same as the difference of next two terms
$\therefore$ $13-(2k+1)=(5k-3)-13$
$⟹$ $13-2k-1=5k-3-13$
$⟹$ $12-2k=5k-16$
$⟹$ $28=7k$
$\therefore$ $k=4$