Question

between 1 and 31 are inserted m atrthimetic means so that ratio of 7 and (m-1) means is 5:7 then value of m is

Answer 1

Answer:

m=14

Step-by-step explanation:

m AM,s are inserted between 1 and 31

then 31 is m+2 th term of AP

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

31=1+(m+1)d

d=30/m+1

M7/Mm-1=5/7

M7=1+7d=1+210/m+1=(m+211)/m+1

Mm-1=1+(m-1)d=1+30(m-1)/m+1=31-29/m+1

M7/Mm-1=[(m+211)/m+1] / [ (31-29)/m+1 ]=5/7

m+211/31m-29=5/9

5*(31m-29)=9*(m+211)

155m-145=9m+1899

155m-9m=1899+145

146m=2044

m=2044/144

=14