Math, asked by superfrooti226, 1 month ago

If 8 arithmetic means are inserted between the numbers 1/3 and 1/2 then find the 2nd term….. please answer only if u know.

Answers

Answered by Swarup1998

The 2nd term of the A.P. with first term 1/3 and the last term 1/2 is 13/27.

The 2nd mean between 1/3 and 1/2 is 25/54.

Let the 8 arithmetic means between 1/3 and 1/2 are x1, x2, x3, x4, x5, x6, x7, x8.

Then 1/2, x1, x2, x3, x4, x5, x6, x7, x8, 1/3 are in A.P.

The first term of the A.P. = 1/2 and the 10th term is 1/3.

Let the common difference be d.

Then 1/2 + (10 - 1) d = 1/3

or, 1/2 + 9d = 1/3

or, 9d = 1/3 - 1/2

or, 9d = (2 - 3)/6

or, 9d = - 1/6

or, d = - 1/54

We have to find the 2nd term of the A.P.

Thus x1 = 1/2 + (2 - 1) d, since x1 is the second term of the A.P. 1/2, x1, x2, ... ..., x8, 1/2

or, x1 = 1/2 + (- 1/54)

or, x1 = 1/2 - 1/54

or, x1 = (27 - 1)/54

or, x1 = 26/54

or, x1 = 13/27

We have to find the 2nd mean.

Thus x2 = 1/2 + (3 - 1) d, since x2 is the third term of the A.P. 1/2, x1, x2, ... ..., x8, 1/3

or, x2 = 1/2 + 2 (- 1/54)

or, x2 = 1/2 - 1/27

or, x2 = (27 - 2)/54

or, x2 = 25/54