# 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.

Given that: Sq= 63q – 3q2

Put q = 1

S1 = T1 = 63 – 3 = 60

Put q = 2

S2 = 63 * 2 – 3 * (2)2

= 126 – 12 = 114

T2 = S2 – S1 = 114 – 60 = 54

Put q = 3

S3 = 63 * 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

Tp = a + (p – 1) d

-60 = 60 + (p – 1) (-6)

-120 = (p – 1) (-6)

(p – 1) = 20

p = 21

Now 11th term of this A.P

T11 = 60 + (11 – 1) (-6)

= 60 – 60 = 0

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