If the `n`th terms of the two AP's 9, 7, 5, … and 24, 21, 18, … are the same, then find the value of `n`. Also, that term.

Explanation

For first A.P. 9,7,5,...
`a=9`
`d=7-9=5-7=-2`
`:. T_(n)=a+(n-1)d`
`=9+(n-1)(-2)`
`=9-2n+2=11-2n " " ...(1)`
For 2nd A.P. 24,21,18,...
`a=24`
`d=21-24=18-21=-3`
`:. T_(n)=a+(n-1)d`
`=24+(n-1)(-3)`
`=24-3n+3=27-3n " " ...(2)`
According to the given condition
`11-2n=27-3n" "` [from (1) and (2)]
`rArr n=16`
Now `T_(16)=11-2xx16 " "` [from(1)]
`=11-32=-21`