Question

the sum of first q terms is 63 q-3q2 . if pth term is -60. find p and also find 11th term of ap

Answer 1

Given, Sq = 63q - 3q^2...........(1)
Put q = 1
S1 = 63(1) - 3(1)^2
S1 = a = 63 - 3 = 60
a = 60......(2)
put q = 2 in (1)
S2 = 63(2) - 3(2)^2
S2 = a + a2 =126 - 12 = 114
a + a2 = 114
using (2)
60 + a2 = 114
a2 = 114 - 60 = 54
d = a2 - a = 54 - 60 = -4
Now ap= -60
ap can be written as a+(p-1)d
a+(p-1)d = -60
60 + (p-1) (-4) = -60
p-1 = -120/-4
p= 30 + 1 = 31
an = a+(n-1)d
a11 = 60 + (11-1)(-4) = 60 + (10)(-4) = 60 - 40 = 20