Question

Let fourth therm of an arithmetic progression be 6 and `m^(th)` term be 18. If A.P has intergal terms only then the numbers of such A.P s is `"____________"`

Answer 1

Correct Answer - 9
Given that `T_(4)=a+3d=6`
and `T_(m)=a+(m-1)d=18`
`rArr(m-4)d=12`
Since terms are integers, we have
`(m-4)=pm1,pm2,pm3,pm4,pm6,pm12`
But `mgt0`.
`therefore(m-4)=pm1,pm2,pm3,4,6,12`.
So, m has nine possible values.