28 arithemetic means are inserted between a and b so that the two means exactly at the middle are 59 and 63 find a and b

Question

This question is from arothemetic mean of optional mathematics

Answer 1

33 35 37 39 41 43 45 47 49 51 53 55 57 59 63 65 67 69 71 73 75 77 79 81 83 85 87 89

So a=33 and b=89.

Answer 2

solution:

no of means(N)=28

so,no of terms must be 30

m15 and m14 are middle one

common difference(d)=b-a/n+1

                                 =b-a/29.................................(i)

m14=28

a+14d=59...............(iI)

m15=63

a+15d=63................(iIi)

(ii)-(i) then

d=4 put value of d in eqn (Ii)

a+15*4=63

or,a+60=63

or,a=63-60

a=3 ans

putting the value of d in eqn (i)

4=b-a/29

crooss multiply on both sides

b-a=116

or,b-3=116

0r,b=116+3

thus b=119 ans

here u go you