Question

if sn=4n-n2 find its a nth term and 20 th term
first to answer will be marked brainly!!

Answer 1

Answer:

nth term is (5 - 2n)  and 20th term is -35

Step-by-step explanation:

Given :

Sum of first n terms of Arithmetic Progression is 4n - n²

To find :

the nth term and 20th term

Solution :

Sₙ = 4n - n²

Sₙ is the sum of first n terms

Put n = 1,

S₁ = 4(1) - 1²

S₁ = 4 - 1

S₁ = 3

This is equal to the first term of Arithmetic Progression

Similarly,

when we put n = 2, the result is equal to the sum of the first term and the second term

S₂ = a₁ + a₂

4(2) - 2² = 3 + a₂

8 - 4 = 3 + a₂  

4 = 3 + a₂  

a₂ = 4 - 3  

a₂ = 1

The second term is 1

We know,

common difference, d = a₂ - a₁

d = 1 - 3  

d = -2

nth term of an AP is given by,

aₙ = a + (n - 1)d

aₙ = 3 + (n - 1)(-2)

aₙ = 3 - 2n + 2

aₙ = 5 - 2n

∴ nth term is (5 - 2n)

We also have to find the 20th term,

put n = 20 in the above expression,

a₂₀ = 5 - 2(20)

a₂₀ = 5 - 40

a₂₀ = -35

∴ 20th term is -35