Q20 of 178 Page 559

Which term of the AP 72, 63, 54, ... is 0?

In the given AP, the first term = a = 72

Common difference = d = 63 - 72 = - 9

To find: place of the term 0.

So, let a_n = 0

Since, we know that

a_n = a + (n - 1) × d

∴ 0 = 72 + (n - 1) × (-9)

⇒ - 72 = - 9n + 9

⇒ - 72 - 9 = - 9n

⇒ - 9n = - 81

⇒ n = 9

∴ 9^th term of the AP is - 81.

What is the common difference of an AP in which a₁₈ – a₁₄ = 32?

If a_n denotes the nth term of the AP 3, 8, 13, 18, ... then what is the value of (a₃₀ - a₂₀)?

Which term of the AP 25, 20, 15, ... is the first negative term?

Which term of the AP 21, 42, 63, 84, ... is 210?