The sum of first q terms of an A.P. is 63q – 3q². If its p^th term is -60, find the value of p. Also find the 11^th term of this A.P.

The sum of first q terms = 63q – 3q²

Putting q = 1, we get

S₁ = 63(1) – 3(1)² = 60

Putting q = 2, we get

The sum of first two terms = S₂ = 63(2) – 3(2)² = 114

⸫ The second term = 114 – 60 = 54

Putting q = 3, we get

S₃ = 63(3) – 3(3)² = 162

⸫ The third term = 162 – 114 = 48

⸫ The first term = a = 60

⸫ The common difference = d = 6

The formula to find the n^th term of an A.P. is given by,

a_n = a + (n – 1) d

⇒ a_p = a + (p – 1) d = -60

⇒ 60 + (p – 1) 6 = -60

⇒ 6p – 6 = 120

⇒ 6p = 126

⸫ p = 21

a₁₁ = 60 + (11 – 1) 6 = 0