Question

There are n Arithmetic means between 3 and 27. if ratio of the 3rd Arithmetic mean and (n -1)tg arithmetic mean be 1:5 then find n

Answer 1

Step-by-step explanation:

suppose A1 A2 A3 ............An are n terms between 3 and 27. Therefore,

3,A1,A2,A3,............An,27 are in arithmetic progression,where the first term a=3 and the(n+2)th term is 27.

suppose common difference of A.P is d

Then(n+2)th term=2u

3+( n+2-1)d= 27

3+(n+1)d=27

(n+1)d=27-3

(n+1)d=24

d=24/n+1

A.T.Q

3rd mean term. =1

nth term of the series. 5

a+3d =. 1

a+(n+1)d. 5

5(a+3)d = a+(n-1)d

5a+15d= a+(n-1)d

5a-a=(n-1)d -15d

4a=(n-1-15)d

4a=(n-14)d

4(3)=(n-14)24

n+1

(putting the value of a and d)

12(n+1)=24(n-14)

12n+12= 24n-336

12+336=24n-12n

348=12n

348 = n

12

29 =n

answer

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