Question

Check whether, -150 is a term of the AP: 11, 8, 5, 2…

Answer 1

Given: A.P. = 11, 8, 5, 2… 

Here a₁ = a = 11; 

d = a₂ – a₁ = 8 – 11 = -3 

If possible, take – 150 as the n^th term of the given A.P. 

a_n = a + (n – 1) d 

⇒ -150 = 11 + (n – 1) × (-3) 

⇒ -150 = 11 – 3n + 3 

⇒ 14 – 3n = – 150 

⇒ 3n= 14 + 150 = 164 

∴ n = \(\frac{164}{3}\) = 54\(\frac{2}{3}\) 

Here n is not an integer. 

∴ -150 is not a term of the given A.P.