Answer:
- S7 = 175
- S17 = 2465
- Sn = 1/2(n³ +n)
Step-by-step explanation:
The progression of sums is ...
1, 5, 15, 34, 65, ...
So, first differences are ...
4, 10, 19, 31
Second differences are ...
6, 9, 12, ...
Third differences are constant:
3, 3, ...
This means the expression for Sn will be a cubic expression. If dn is the first of the n-th differences, then the equation can be written as ...
Sn = S1 +(n -1)(d1 +(n -2)/2(d2 +(n -3)/3(d3)))
And this simplifies a little bit to ...
Sn = 1 +(n -1)(4 +(n -2)(n +3)/2)
In simpler form, we have ...
Sn = 1/2(n³ +n)
Then the two terms we're interested in are ...
S7 = (1/2)(7³ +7) = 175
S17 = (1/2)(17³ +17) = 2465
Answer:
40 units
Step-by-step explanation:
An octagon is a polygon with 8 sides. A regular octagon is an octagon in which all their sides and angles are equal to each other.
Since the vertices of a regular octagon are located at (1, 4) and (4,8), hence the length of the side is gotten using the formula for calculating the distance between two points 
.
Hence:
Since all the sides of a regular octagon are equal, therefore:
Perimeter = 8 × length = 8 × 5 = 40 units
10,10,11,11,12,12,14,15,16,18,18,19
10,10,10,11,11,12,12,14,15,16,18,18,19
10,10,11,11,11,12,12,14,15,16,18,18,19
10,10,11,11,12,12,12,14,15,16,18,18,19
10,10,11,11,12,12,14,15,16,18,18,18,19
I THINK it's D
The standard form of the equation of a circle of radius r, with (assuming centre h, k) is given as:
(X-h)^2 + (y-k)^2 = r^2
As we are required to write an equation in standard form for the circle with radius 9 centred at the origin.
Centre(h,k)=(0,0), r=9
Substituting these values into the standard form of the equation of a circle given above:
(X-0)^2 + (y-0)^2 = 9^2
X^2 + y^2 =81
The standard form is x^2 + y^2 =81
I’m pretty sure this is right
