If the 20th term of a H.P. is 1 and the 30th term is -1/17, then find its largest term.

Explanation

Let the H.P be `1/a,1/(a+d),1/(a+2d),1/(a+3d),…` We have,
`a_(20)=1 anda_(30)=-1/17`
`rArr1/(a+19d)=1 and 1/(a+29d)=-1/17`
`rArra+19d=1anda+29d=-17`
`rArra=176/5,d=-9/5`
Le nth term be the largest term. We have,
`a_(n)=1/(a+(n-1)d)`
`=1/(176/5+(n-1)((-9)/(5)))`
`=5/(176-9(n-1))`
`=5/(185-9n)`
now,`a_(n)` is the largest term if 185-9n is the least positive integer.