Question

For what value of k will the consecutive term 2k + 1, 3K+ 3 and 5 k - 1 from an A.P

Answer 1

lets say first term a1 = 2k + 1 , second term a2 = 3k + 3 and third term a3 = 5k - 1

For a1 , a2 , and a3 to be in A . P ,

   common difference d = a2 - a1 = a3 - a2

⇒ (3k + 3) - ( 2k + 1 ) = (5k -1) - ( 3k + 3)

⇒  k + 2 = 2k - 4

⇒ k = 6

hence for k = 6 , A P 13 , 21 , 29 will form.