Which term of A.P., 100, 97, 94, 91, will be its first —ve term?

We have the A.P as 100, 97, 94, 91 …

So, a = 100

⇒ d= 97 – 100 = – 3

Now recall that, nth term of an AP is T_n = a + (n – 1)d

⇒ T_n = 100 + (n – 1)(– 3)

= 100 – 3n + 3

⇒ T_n = 103 – 3n

Since we need negative term, T_n < 0

So, 103 – 3n < 0

⇒ 103 < 3n

⇒ < n

⇒ 34.333 < n

⇒ n>34

i.e. N = 35

∴ n=35 for the first negative term in the given A.P.

⇒ T₃₅ = a + (35 – 1)d

= 100 + 34 × – 3

= 100 – 102

= – 2

∴ the first negative term of the given AP is – 2.