If 11 arithmetic means are inserted between 28 and 10 , then the number of integral arithmetic means are

Step-by-step solution

Let, A 1 , A 2 , A 3 , … … , A 11 be 11 A.M.’s between 28 and 10 ⇒ 28 , A 1 , A 2 , … … , A 11 , 10 are in A.P Let, d be the common difference of A.P. Also, the number of terms = 13 ⇒ 10 = T 13 = T 1 + 12 d = 28 + 12 d ⇒ d = 10 - 28 12 = - 18 12 = - 3 2 ⇒ Number of integral A.M.’s are 5