If the sum of first n terms of an AP is 4n-n² what is the first (remember the first term is s₁)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd,and the 10th and the nth terms.

Question

Philoid · Accepted Answer

The sum of first n terms is given by 4n –n²

So the first term is

a₁ = 4(1) – 1² = 3

the sum of first two term S₂ = 4(2) – 2² = 4

The difference between S₂ & S₁ gives us 2^nd term

a₂ = S₂ - S₁ = 4-3 = 1

the sum of first 3 term S₃ = 4(3) – 3² = 3

The difference between S₂ & S₃ gives us 3^rd term

a₃ = S₃ – S₂ = 3-4 = -1

From this we can find common difference = a₂ – a₁ = 1-3 = -2

So the 10^th term is = a + (10-1)d

= 3 + 9×(-2) = -15

n^th term is = a + (n-1)d

= 3 + (n-1)×(-2) = 5 -2n

If the sum of first n terms of an AP is 4n-n2 what is the first (remember the first term is s1)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd,and the 10th and the nth terms.