If the sum of the first n terms of an AP is 4n – n², what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.

The sum of n terms of an AP is given by
S_n = 4n – n²
Putting n = 1, we get
First term = a₁ = S₁ = 4(1) – (1) ² = 3
Putting n = 2, we get
sum of two terms = a₁ + a₂ = S₂ = 4(2) -(2)² = 4
⇒ a₁ + a₂ = 4
⇒ 3 + a₂ = 4 [∵ the first term a₁ = 3 ]
⇒ a₂ = 1
Hence, the second term is 1.
Common difference d = a₂ – a₁ = 1 – 3 = – 2
Therefore, the tenth term = a_10 = a + 9d = 3 + 9(-2) = – 16
Similarly, the nth term = a_n = a + (n -1)d = 3 + (n -1)(-2) = 5 – 2n