Answer:

the sum of the first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.

Solution:

The sum of the first n terms of an AP is given by Sₙ = n/2 [2a + (n - 1) d] or Sₙ = n/2 [a + l], and the nth term of an AP is aₙ = a + (n - 1)d

Here, a is the first term, d is the common difference and n is the number of terms and l is the last term.

Given,

Sum of first n terms, Sₙ = 4n - n²

Therefore,

Sum of first term, S₁ = 4 × 1 - 1² = 4 - 1 = 3

Sum of first two terms, S₂ = 4 × 2 - 2² = 8 - 4 = 4

Sum of first three terms, S₃ = 4 × 3 - 3² = 12 - 9 = 3

Second term, a₂ = S₂ - S₁ = 4 - 3 = 1

Third term, a₃ = S₃ - S₂ = 3 - 4 = - 1

Tenth term, a₁₀ = S₁₀ - S₉

= (4 × 10 - 102) - (4 × 9 - 92)

= (40 - 100) - (36 - 81)

= - 60 + 45

= - 15

nth term, aₙ = Sₙ - Sₙ₋₁

= [4n - n²] - [4 (n - 1) - (n - 1)² ]

= 4n - n² - 4n + 4 + (n - 1)²

= 4 - n² + n² - 2n + 1

= 5 - 2n