Question

Which term of the progression 20, 191/4, 181/2, 173/4 ,... is the first negative 4 term?

Answer 1

the answer is 45353453445

Answer 2

Question :

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

Solution :

The given sequence is an arithmetic progression in which the first term (a) is 20 and the common difference (d) is $\frac{-3}{4}$.

Let the nth term of the given A.P be the first negative term. Then $a_n$ < 0.

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

$20+(n-1)(\frac{-3}{4})<0$

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

$83-3n<0$

$3n<83$

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

∴ $n=28$

Thus, 28th term of the given sequence is the first negative term.