Question

Which term of the sequence $20,19\frac{1}{4},18\frac{1}{2},17\frac{3}{4}$,... is the first negative term ?

• A. 25
• B. 28
• C. 30
• D. 35

Answer 1

The correct option is B 28

The given sequence is an A.P. in which first term $a=20$ and common difference $d=-\frac{3}{4}$. Let the nth term of the given A.P. be the first negative term. Then,

$a_n<0$

$a+(n-1)d<0$

$20+(n-1)\times (-3/4)<0$

$\frac{83}{4}-\frac{3n}{4}<0$

$83-3n<0$

$3n>83$

$n>27\frac{2}{3}$

Since 28 is the natural number just greater than $27\frac{2}{3}$. So, $n=28$. Thus, 28th term of the given sequence is the first negative term.