Question

The middle term of the AP 11, 8, 5, …  ,  -79 will be?

(a) 30

(b) -34

(c) 34

(d) -30

This question was addressed to me in my homework.

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

Answer 1

The correct choice is (b) -34

The explanation is: Here a = 11 and d = 8 – 11 =  -3

Let the given AP contain n terms.

Tn = -79

a + (n – 1)d = -79

11 + (n – 1) – 3 = -79

11 – 3n + 3 =  -79

14 + 79 = 3n

n = 31

Thus, the given AP has 31 terms.

∴ its middle term =  \(\frac {1}{2}\) (31 + 1) = 16^th term

∴ 16^th  term = 11 + (16 – 1) – 3 = 11 – 45 =  -34