Question

Which term of the AP 80, 76, 72, 68……. is the first negative term?

(a) 22

(b) 21

(c) 23

(d) 24

I got this question in an interview.

I'd like to ask this question from Arithmetic Progression Basics in division Arithmetic Progressions of Mathematics – Class 10

Answer 1

Right option is (a) 22

To explain I would say: Here a = 80 and d = 76 – 80 =  – 4

Let Tn be the first negative term of the given AP.

Tn < 0

a + (n – 1)d < 0

80 + (n – 1) – 4 < 0

80 – 4n + 4 < 0

84 < 4n

n > 21

Hence the 22^th term of the given AP will be its first negative term.