Which term of the AP 24, 21, 18, 15, ………. is the first negative

1.	Which term of the AP 24, 21, 18, 15, ………. is the first negative term?
Answer» Given, AP is 24, 21, 18, 15, …… First term of AP is a = 24. Common difference of AP is d = a₂ − a₁ = 21 − 24 = −3. Since, First term is 24 which is multiple of 3 and common difference is – 3. Therefore, All terms of AP are multiple of 3. ∴ First negative term of given AP is – 3. Let n^th term of AP is – 3. ∴ a + (n − 1)d = −3 (∵ n th term of AP is given by an = a + (n − 1)d) ⇒ 24 + (n − 1) × −3 = −3 (∵ a = 24 & d = −3) ⇒ −3(n − 1) = −3 − 24 = −27 ⇒ n −1 = \(\frac{-27}{-3}\) = 9 ⇒ n = 1 + 9 = 10. Hence, 10th term of given AP is the first negative term.

Which term of the AP 24, 21, 18, 15, ………. is the first negative term?

Answer»

Given,

AP is 24, 21, 18, 15, ……

First term of AP is a = 24.

Common difference of AP is d = a₂ − a₁

= 21 − 24 = −3.

Since,

First term is 24 which is multiple of 3 and common difference is – 3.

Therefore,

All terms of AP are multiple of 3.

∴ First negative term of given AP is – 3.

Let n^th term of AP is – 3.

∴ a + (n − 1)d = −3

(∵ n th term of AP is given by an = a + (n − 1)d)

⇒ 24 + (n − 1) × −3 = −3

(∵ a = 24 & d = −3)

⇒ −3(n − 1)

= −3 − 24

= −27

⇒ n −1 = \(\frac{-27}{-3}\) = 9

⇒ n = 1 + 9 = 10.

Hence,

10th term of given AP is the first negative term.

Discussion

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