Question

Between 1 and 31, m number have been inserted in such a way that the resulting sequence is an
a.P. And the ratio of 7th and (m-1)th number is 5:9. Find the value of m.

Answer 1

Answer:

m=5/9

Step-by-step explanation:

AP of this series = 1, A1 ,A2, A3 ....Am , 31

Here,

a=1 , an=31 and n= m+2

an=a+(n-1)d

31=1+(m+2-1)d

30=(m+1)d

d=30/(m-1)

 Now,

A1=a+d = 1+30/(m-1)

A2=a+2d = 1+2[20/(m-1)]

A7=a+7d = 1 +7[20/(m-1)]  -1

Am-1=a+(m-1)d = 1+(m-1)[20/(m-1)]  -2

Now, from 1 and 2  

A7/Am-1 = 5/9

1 +7[20/(m-1)/1+(m-1)[20/(m-1)] =5/9

m=5/9