Question

Which term of the sequence 17, $16\frac{1}{5},15\frac{2}{5},14\frac{3}{5},...$ is the first negative term?

• A. ${23}^{rd}$
• B. $3^{rd}$
• C. ${33}^{rd}$
• D. None of these

Answer 1

The correct option is A ${23}^{rd}$

Since, first term a=17 and comman difference d=$16\frac{1}{5}-17=\frac{81}{5}-17=-\frac{4}{5}$
Let $n^{th}$ term be the first negative term.
$a_n<0$
a + (n - 1)d < 0
17 + (n - 1) - $\frac{4}{5}$ < 0
17 - $\frac{4}{5}$n + $\frac{4}{5}$ < 0
n < $\frac{89}{4}$
n < 22$\frac{1}{4}$
So, ${23}^{rd}$ term will be the first negative term.