Which term of the progression $20,\ 19\frac{1}{4} ,\ 18\frac{1}{2} ,\ 17\frac{3}{4} ,\ .............$ is the first negative term ?
Given: The progression $20,\ 19\frac{1}{4} ,\ 18\frac{1}{2} ,\ 17\frac{3}{4} ,\ .............$
To do: To find the the first negative term of the given progression.
Solution:
Given progression $20,\ 19\frac{1}{4} ,\ 18\frac{1}{2} ,\ 17\frac{3}{4} ,\ .............$
This is an Arithmetic progression because Common difference $( d) \ =19\frac{1}{4} -20=18\frac{1}{2} -9\frac{1}{4}$
$d=\frac{-3}{4}$
Any term $a_{n} =20\ ( n-1) d=20\ ( n-1)\frac{-3}{4}$
Any term $a_{n} < 0$ when $83\ < 3n\ $
This is valid for $n=28$ and $28^{th}$ term will be the first negative term.
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