Question

There are nAM's between 1 and 31 such that 7th mean:(n-1)th mean =5:9 then find the value of n

Answer 1

Answer:

n=14

Step-by-step explanation:

Let a1, a2, a3, .... an be n numbers such that 1, a1, a2, a3, .... an, 31 is an A.P.

m be the total number of terms in A.P.

here a = 1, b = 31, m = n+2

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

30 = (n + 1) d

d = 30/(n + 1)

so,

a7=a+7d

an-1 = a + (n-1)d

ATS,

(a+7d)/[a + (n-1)d] =5/9

[1+7(30/n+1)]/[1 + (n-1)(30/n+1)] = 5/9

after solving above equation, we have

n = 14

the the value the n is 14.