The sum of first q terms of an A.P. is 63q – 3q2. If its pth term is

1.	The sum of first q terms of an A.P. is 63q – 3q2. If its pth term is -60, find the value of p. Also, find the 11th term of this A.P.
Answer» Given that: S_q= 63q – 3q² Put q = 1 S₁ = T₁ = 63 – 3 = 60 Put q = 2 S₂ = 63 x 2 – 3 x (2)² = 126 – 12 = 114 T₂ = S₂ – S₁ = 114 – 60 = 54 Put q = 3 S₃ = 63 x 3 – 3(3)² = 189 – 27 = 162 T₃ = S₃ – S₂ = 162 – 114 = 48 Therefore, first term of this A.P. is 60 and Common difference is 54 - 60 = -6 T_p = a + (p – 1) d -60 = 60 + (p – 1) (-6) -120 = (p – 1) (-6) (p – 1) = 20 p = 21 Now 11^thterm of this A.P T₁₁ = 60 + (11 – 1) (-6) = 60 – 60 = 0

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

Answer»

Given that:

S_q= 63q – 3q²

Put q = 1

S₁ = T₁ = 63 – 3 = 60

Put q = 2

S₂ = 63 x 2 – 3 x (2)² = 126 – 12 = 114

T₂ = S₂ – S₁ = 114 – 60 = 54

Put q = 3

S₃ = 63 x 3 – 3(3)²

= 189 – 27 = 162

T₃ = S₃ – S₂

= 162 – 114 = 48

Therefore, first term of this A.P. is 60 and Common difference is 54 - 60 = -6

T_p = a + (p – 1) d

-60 = 60 + (p – 1) (-6)

-120 = (p – 1) (-6)

(p – 1) = 20

p = 21

Now 11^thterm of this A.P

T₁₁ = 60 + (11 – 1) (-6)

= 60 – 60 = 0