Question

Suppose m arithmetic means are inserted between 1 and 31. If the ratio of the second mean to the mth mean is 1 : 4, then m is equal to :

Answer 1

Answer:

m equal to 9

pic gives explanation

Answer 2

Answer:

m = 9

Step-by-step explanation:

Suppose m arithmetic means are inserted between 1 and 31. If the ratio of the second mean to the mth mean is 1 : 4, then m is equal to

m terms are inserted between

1 & 31  

then total terms = m + 2

2nd mean = 3rd term  = 1 + 2d

mth Mean = m + 1 th term = 1 + md

(1+ 2d) : ( 1 + md) = 1 :4

=> (1 + 2d)/(1 + md) = 1/4

=> 4 + 8d = 1 + md

=> d(m-8) = 3

=> d = 3/(m-8)

Last term = a + (m+2 - 1)d

=> 1 + (m+1)d = 31

=> 1  + (m+1)3/(m-8) = 31

=> 3(m+1) = 30 (m-8)

=> m + 1 = 10(m-8)

=> m + 1 = 10m - 80

=> 9m = 81

=> m = 9