Question

If $k,2k-1$ and $2k+1$ are three consecutive terms as an $A.P.$ then find the value of $k$.

• A. $2$
• B. $3$
• C. $-3$
• D. $5$
• E. $4$

Answer 1

The correct option is B $3$

$k,2k-1,2k+1$ are three terms in A.P. Then,
Common difference between first two terms = $2k-1-k$ =$k-1$
Common difference between next two terms = $2k+1-2k+1$ =$2$
The common difference between consecutive terms should be equal.
Hence, $k-1=2$
$k=3$