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

Options

A. 27th
B. 28th
C. 29th
D. No such term exists

Answer

B

Explanation

Given sequence is `20,19(1)/(4),18(1)/(2),17(3)/(4),….`
Which can be rewritten as `20,(77)/(4),(37)/(2),(71)/(4),..`
This is an AP seriies.
Here, first term a=20 and common difference `d = -(3)/(4)`
`n^(th)" term"=a+(n-1)d=20+(n-1)(-(3)/(4))`
`=(83)/(4)-(3)/(4)n`
For first negative term, `n^(th)` term `lt0`
`implies(83)/(4)-(3)/(4)nlt0implies83lt3n`
`impliesngt(83)/(3)=27.66`
So, in should be 28.
Hence, 28th term is first negative term.