Which term of the A.P. `10, 9(1)/(3), 8(2)/(3)= -(2)/(3), ..... ` is the first negative term ?

Explanation

Here, a=10,
`d=9(1)/(3)-10=8(2)/(3)-9(1)/(3)=-(2)/(3)`
Let `a_(n) lt 0`
`rArr 10+(n-1)(-(2)/(3)) lt 0`
`rArr (30-2n+2)/(3) lt0`
`rArr 32-2n lt 0 rArr 32 lt 2n`
`rArr 2n gt 32 rArr n gt 16`
`rArr n=17, 18, 19, .....` (all are negative terms)
`:. ` First negative term =17th term.
Now, `a_(17)=a+(17-1)d`
`=10+16(-(2)/(3))=10-(32)/(3)=(-2)/(3)`
Thus, 17th term which is `-(2)/(3)` is the first negative term.