Which term of the A.P. 84, 80, 76,… is 0?

1.	Which term of the A.P. 84, 80, 76,… is 0?
Answer» Given, A.P is 84, 80, 76,… Here, a₁ = a = 84, a₂ = 88 Common difference, d = a₂ – a₁ = 80 – 84 = -4 We know, a_n = a + (n – 1)d Where a is first term or a₁ and d is common difference ∴ a_n = 84 + (n – 1)-4 ⇒ a_n = 84 – 4n + 4 ⇒ a_n = 88 – 4n Now, To find which term of A.P is 0 Put an = 0 ∴ 88 – 4n = 0 ⇒ -4n = -88 ⇒ n = \(\frac{-88}{-4}\) ⇒ n = 22 Hence, 22^th term of given A.P is 0.

Answer»

Given,

A.P is 84, 80, 76,…

Here,

a₁ = a = 84,

a₂ = 88

Common difference,

d = a₂ – a₁

= 80 – 84

= -4

We know,

a_n = a + (n – 1)d

Where a is first term or a₁ and d is common difference

∴ a_n = 84 + (n – 1)-4

⇒ a_n = 84 – 4n + 4

⇒ a_n = 88 – 4n

Now,

To find which term of A.P is 0

Put an = 0

∴ 88 – 4n = 0

⇒ -4n = -88

⇒ n = \(\frac{-88}{-4}\)

⇒ n = 22

Hence,

22^th term of given A.P is 0.

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