The Total solution for NCERT class 6-12
Between 1 and 31, m numbers have been inserted in such away that the resulting sequence is an A.P. and the ratio of 7th and(m – 1)th numbers is 5: 9. Find the value of m.
Let’s consider a1,a2, … am be m numbers suchthat 1, a1, a2, … am, 31 is an A.P.
And here,
a = 1, b = 31, n = m +2
So, 31 = 1 + (m +2 – 1) (d)
30 = (m +1) d
d = 30/ (m + 1) …….(1)
Now,
a1 = a + d
a2 = a +2d
a3 = a +3d …
Hence, a7 = a +7d
am–1 = a +(m – 1) d
According to thequestion, we have
Therefore, the valueof m is 14.