Solution:
Given, Sn = 4n – n2
Therefore, S1 = 4(1) – (1)2 = 4 – 1 = 3 (Answer)
And S2 = 4(2) – (2)2 = 8 – 4 = 4
∴ Second term = a2
= S2 – S1 [∵ an = Sn – Sn – 1]
= 4 – 3
= 1 (Answer)
Similarly, S3 = 4(3) – (3)2 = 12 – 9 = 3(Answer)
S9 = 4(9) – (9)2 = 36 – 81 = -45
S10 = 4(10) – (10)2 = 40 – 100 = -60
Therefore,
Third term = a3 = S3 – S2 [∵ an = Sn – Sn – 1]
= 3 – 4
= -1 (Answer)
Tenth term = a10 = S10 – S9 [∵ an = Sn – Sn – 1]
= -60 – (-45)
= -60 + 45
= -15 (Answer)
nth term = an = Sn – Sn – 1
= 4n – n2 – {4(n – 1) – (n – 1)2}
= 4n – n2 – {4n – 4 – (n2 – 2n + 1)}
= 4n – n2 – {4n – 4 – n2 + 2n – 1}
= 4n – n2 – (- n2 + 6n – 5)
= 4n – n2 + n2 – 6n + 5
= 5 – 2n (Answer)