First slide

Arithmetic progression

Question

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

Moderate

A

27
B

28
C

29
D

30

Solution

The given sequence is an A.P in which first term a=20 and common difference d=-3/4. Let the nth term of the given A.P. be the first negative term. Then,
$a_{n} < 0 \Rightarrow a + (n - 1) d < 0 \Rightarrow 20 + (n - 1) (- 3 / 4) < 0$
$\Rightarrow \frac{83}{4} - \frac{3 n}{4} < 0 \Rightarrow 83 - 3 n < 0 \Rightarrow 3 n > 83 \Rightarrow n > 27 \frac{2}{3} \Rightarrow n = 28$

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