Question

Which term of the sequence `20 , 19 1/4, 18 1/2, 17 3/4, dot` is the first negative term?

Answer 1

The given sequence is an AP in which first term, a=20 and common difference, `d=-(3)/(4).` Let the nth term of he given AP be the first negeive term. Them,
`t_(n)lt 0 implies a+(n-1)dlt0`
`implies 20+(n-1)(-(3)/(4))lt0`
`implies 80-3n+3lt0`
`implies ngt(83)/(3)"or " n27(2)/(3)`
n= 28
Thus, 28th term of the given sequence is the first negetive term.