Question

Which term of an ap 150,147,144. Is its first negative no?

Answer 1

Hey there !!

→ Given :-

→ a₁ = 150.

→ a₂ = 147.

Then, d = a₂ - a₁ .

⇒ d = 147 - 150 = -3.

To find :-

→ n ( first negative term).

Solution :-

Let the nth term of the given AP be the first negative term .

then, Tn < 0 .

⇒ [ a + ( n - 1 )d] < 0.

⇒ [ 150 + ( n - 1) × (-3) ] <0.

⇒ [ 150 - 3n + 3 ] < 0.

⇒ [ 153 - 3n ] < 0.

⇒ 153 < 3n .

⇒ 3n > 153.

⇒ n > 153/3.

⇒ n > 51.

∴ n = 52.

Hence, the 52th term is the first negative term of the given AP.

THANKS

#BeBrainly.

Answer 2

In the AP 150, 147, 144, … the common difference is -3.

The first negative term will be -3.

Tn = a +(n-1)d = -3, or

150 + (n-1)(-3) = -3, or

n-1 = (150+3)/3 = 153/3 = 51, or

n = 52.

The 52nd term will be the first negative term.

Check: T52 = a+(n-1)d = 150 +(52–1)(-3)

= 150 + 51(-3) = 150 - 153 = -3. Correct.