Question

Which term of an the A.P. 150, 147, 144, ..... is the first negative term? Thank you in advance.

Answer 1

Here a = 150, d = 116 – 120 = – 4
nth term of an AP is tn = a + (n – 1)d
= 120 + (n – 1)(– 4)
= 120 – 4n + 4
= 124 – 4n
Since we need negative term, tn < 0
124 – 4n < 0
⇒ 124 < 4n
⇒ 31 < n
That is n > 31
Hence n = 42
Therefore the 42nd term is first negative term.

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the nth term be 0.

Then,

⇒ a(n) = 0

⇒ a + (n - 1)d = 0

⇒ 150 + (n - 1)(- 3) = 0

⇒ 150 - 3n + 3 = 0

⇒ - 3n = - 153

⇒ n = 51

Hence, the first negative term is 52 nd Term.