Question

If k, (2k- 1) and (2k + 1) are the three successive terms of an AP, find the value of k.

Answer 1

If a,b, c are in Ap
$b-a=c-b$-----(1)

According to the given problem
$a=k,b=2k-1,c=2k+1$
Using (1)

$(2k-1)-k=(2k+1)-(2k-1)$
$2k-1-k=2k+1-2k+1$
$k-1=2$
$k=2+1$
$k=3$