Question

There are n A.M's between 3 and 17. The ratio of the last mean to the first mean is 3:1. Find the value of n​

Answer 1

3,A

1

,A

2

,.....A

n

,17

a

n

=a+(n−1)d

inourcasea

n

=17,a=3andnumberofterms=(n+2)

∴17=3+[(n+2)−1]d

17−3=(n+1)d

∴d=

n+1

14

Now,A

1

=a+d=3+

n+1

14

andA

n

=a+nd=a+n

n+1

14

asgiveninquestion

A

1

A

n

=

1

3

Or

3+

n+1

14

3+

n+1

14n

=3

3(n+1)+14

3(n+1)+14n

=3

3n+17

17n+3

=3

17n+3=3(3n+17)

17n+3=9n+51

8n=48

∴n=6