If the sum of the first n terms of an A.P. is 4n – n 2 , which is the first term? What is the sum of first two terms? What is the second term? Similarly, find the third, the tenth and the nth terms.

Question

If the sum of the first n terms of an A.P. is 4n &#x2013; n 2 , which is the first term? What is the sum of first two terms? What is the second term? Similarly, find the third, the tenth and the nth terms.

Philoid · Accepted Answer

Given, S_n = 4n – n²

Putting n = 1, 2

S₁ = 4(1) – (1)² = 3

S₂ = 4(2) – (2)² = 4

We know, a_n = S_n – S_{n – 1}

For first term, a₁ = S₁ – S₀ = 3 – 0 = 3

For term a₂ = S₂ – S_{1 =}4 – 3 = 1

Now fore term a₃,

S₂ = 4(2) – (2)² = 8 – 4 = 4

S₃ = 4(3) – (3)² = 12 – 9 = 3

a₃ = S₃ – S₂ = 3 – 4 = -1

If the sum of the first n terms of an A.P. is 4n – n2, which is the first term? What is the sum of first two terms? What is the second term? Similarly, find the third, the tenth and the nth terms.

If the sum of the first n terms of an A.P. is 4n – n², which is the first term? What is the sum of first two terms? What is the second term? Similarly, find the third, the tenth and the nth terms.