Question

Which term of the AP: 53, 48, 43,... is the first negative term?

Answer 1

Given AP is 53, 48, 43,…

Whose first term (a) = 53 and

Common difference (d) = 48 – 53 = –5

Let n^th term of the AP be the first negative term.

i.e., T_n < 0  .......[∵ n^th term of an AP, T_n = a + (n – 1)d]

⇒ [a + (n – 1 )d] < 0

⇒ 53 + (n – 1)(– 5) < 0

⇒ 53 – 5n + 5 < 0

⇒ 58 – 5n < 0

⇒ 5n > 58

⇒ n > 11.6

⇒ n = 12

i.e., 12^th term is the first negative term of the given AP

∴ T₁₂ = a + (12 – 1)d

= 53 + 11(–5)

= 53 – 55

= – 2 < 0