Which term of the AP 53, 48, 43, … is the first negative term ?

Explanation

Given AP is 53, 48,43, …
Whose, first term (a) = 53 and common difference (d) = 48 - 53 = - 5
Let `n`th term of the AP be the first negative term.
i.e., ` " " T_(n) lt 0 " " ` [ ` :' n`th term of an AP, `T_(n)=a+(n-1)d`]
` " "(a+(n-1)d lt 0`
`implies 53+(n-1)(-5) lt 0`
`implies 53-5n+5 lt 0`
`implies 58-5n lt 0implies 5n gt 58`
`implies n gt 11.6impliesn=12`
i.e., 12th term is the negative term of the given AP.
` :. T_(12)=a+(12-1)d=53+11(-5)`
` " " =53-55= -2 lt 0`