C. 113.04 in'2
STEP 1:
3.14 x 6'2 ~ 113.04
EXPLANATION:
The formula for solving the area of a circle is- 3.14 x r'2
r=radius
We have an arithmetic progression:
an=number of item at row n
an=a₁+(n-1)d
d=common difference=an-a(n-1)=a₂-a₁=2-1=1
n=number of row
In this case:
an=1+(n-1)*1=n
The sum of an arithmetic serie is:
Sn=(a₁+an)n / 2
In this case:
a₁=1 (number of itms in the first row)
an=n (we have to calculate this before)
Sn=(1+n)n /2=(n+n²)/2
Therefore:
f(n)=Sn=number of items when we have n number of rows
f(n)=(n+n²)/2
Answer: f(n)=(n+n²)/2
To chek:
f(1)=(1+1²)/2=1
f(2)=(2+2²)/2=6/2=3
f(3)=(3+3²)/2=(3+9)/2=12/2=6
....
