Insert arithmetic means between 16 and 65 such that the 5th AM is 51. Find the number of arithmetic means.
Insert arithmetic means between 16 and 65 such that the 5th AM is 51. Find the number of arithmetic means.

To find: The number of arithmetic means
Given: (i) The numbers are 16 and 65
(ii) 5th arithmetic mean is 51

Using Formula, An = a + nd
First arithmetic mean, A1 = a + d
= 16 + 7
= 23
Second arithmetic mean, A2 = a + 2d
= 16 + 2(7)
= 16 + 14
= 30
Third arithmetic mean, A3 = a + 3d
= 16 + 3(7)
= 16 + 21= 37
Fourth arithmetic mean, A4 = a + 4d
= 16 + 4(7)
= 16 + 28
= 44
Fifth arithmetic mean, A5 = a + 5d
= 16 + 5(7)
= 16 + 35
= 51
Sixth arithmetic mean, A6 = a + 6d
= 16 + 6(7)
= 16 + 42
= 58
Ans) The six arithmetic means between 1 and 65 are 23, 30, 37, 44, 51 and 58.