Which term of the sequence 24, 231 4 , 221 2 , 213 4 ... is the first negative term?

The given sequence is 24, 231 4 , 221 2 , 213 4 ... Here, a=24 d=231 4 -24=93-96 4 =-3 4 a_n 33 34th term is 1st negetive term.

Which term of the sequence 24, 231 4 , 221 2 , 213 4 ... is the f…

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Question

Which term of the sequence $24,\ 23\frac{1}{4},\ 22\frac{1}{2},\ 21\frac{3}{4}...$ is the first negative term?

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Answer

The given sequence is $24,\ 23\frac{1}{4},\ 22\frac{1}{2},\ 21\frac{3}{4}...$
Here, $\text{a}=24$
$\text{d}=23\frac{1}{4}-24=\frac{93-96}{4}=\frac{-3}{4}$
$\text{a}_\text{n}<0$
$\text{a}+(\text{n}-1)\text{d}<0$
$24-\frac{3}{4}(\text{n}-1)<0$
$96-3\text{n}+3<0$
$99<3\text{n}$
$33<\text{n}$ or $\text{n}>33$
$\therefore$ 34th term is 1st negetive term.

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