Question

Find the middle term of an AP20 16 12.....-180

Answer 1

Given AP is 20,16,12.............[-176]

Here a = 20, d = 16 – 20 = – 4

tn = –176

nth term of an AP is tn = a + (n – 1)d

⇒ –176 = 20 + (n – 1)(– 4)

⇒ –176 = 20 – 4n + 4

⇒ –176 = 24 – 4n

⇒ –176 – 24 = –4n

⇒ –200 = – 4n

∴ n = 50

The middle terms are 25th and 26th terms

t25 = 20 + (25 – 1)(– 4)

= 20 – 96 = –76

t26 = 20 + (26 – 1)(– 4)

= 20 – 100 = –80