Insert A.M.s between 7 and 71 in such a way that the 5^th A.M. is 27. Find the number of A.M.s

Open in App

Solution

Let there be n A.M. between 7 and 71 and let the A.M.s be $A_{1}, A_{2}, A_{3}, \dots \dots A_{n}$

So,

$7, A_{1}, A_{2}, A_{3}, \dots \dots A_{n}, 71$ are in A.P of (n + 2) terms.

$A_{5} = a_{6} = a + 5 d = 27$ [Given]

$\Rightarrow a + 5 d = 27$

$\Rightarrow 5 d = 27 - 7$ $[∵ a = 7]$

$\Rightarrow d = 4$ $[∵ a = 7]$ ..... (i)

The (n+2)th term of A.P. is 71

$∴ a_{n + 2} = 71 = a + (n + 2 - 1) d$

$\Rightarrow 7 + (n - 1) d = 71$

$\Rightarrow 4 n - 4 = 64$

Or $n = 15$

There are 15 A.M's between 7 and 71.

Suggest Corrections

Similar questions

Insert 7 A.M.s between 2 and 17.

If n A.M.s are inserted between 20 and 80 such that first mean:last mean =1:3. Find n

If $9$ A.M.s and $9$ H.M.s are inserted between $2$ and $3$ and $A$ be any A.M. and $H$ be the corresponding H.M.,

then $H (5 - A) =$

Join BYJU'S Learning Program