Question

n² +2n is the algebraic expression for sum of n terms
of an arithmetic sequence when find the nth term of that sequence
​

Answer 1

Step-by-step explanation:

Sn=n/2(2a-d+nd)=n²+2n

n/2(2a-d+nd)=n(n+2)

2a-d+nd=2n+4

nd=2n......... d=2

2a-d=4

2a=6........ a=3

Tn=a+nd-d=3+3n-2=3n+1

Answer 2

Answer:  aₙ = 2n + 1

Step-by-step explanation:

a₁ = Sₙ - S₍ₙ ₋ ₁₎
Sₙ = n² +2n

S₍ₙ ₋ ₁₎ = (n-1)² + 2(n-1) = n² - 2n + 1 +2n - 2 = n² - 1
a₁ = n² + 2n - ( n² - 1 ) = n² + 2n - n² + 1 = 2n + 1

a₁ = 2(1) + 1 = 3
a₂ = 2(2) + 1 = 5
d = a₂ - a₁ = 5 - 3 = 2

Now, General equation

aₙ = a₁ + (n-1)d = 3 + (n-1)2 = 3 + 2n - 2 = 2n + 1

Hope it Helps :)