IIT JEE , AIEEE Forum - Mathematics , Algebra

deedee

if m arithmatic means r inserted btwn 1 & 31 .

so dat d ratio of d 7th & (m-1) th mean is 5:9

then d value of m is........????

chimanshu_007

well...

go frm here

let m means be inserted

A₁ , A₂...........A_m between 1 & 31 ok?

then 1 , A₁ , A₂...........A_m , 31 are in AP

and u might be knowing this formula....d = (b-a) / n + 1

so common diff = 31 - 1 / m + 1= 30 / m + 1

now here the 7th term will nt b 1 + 6d....(as we have 2 more terms (1 and 31) )

so 7th term will be 1 + 7d = 1 + (7*30 / m + 1)

A₇ = m + 211 / m + 1

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

given the ratio of 7th to m-1 terms..hai na

so

jst put the values here

cross multiply

m comes out to be 14

if nt then tell me