The equation for this sequence is:

a_n = a_n-1 + 3

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 3
a₆ = 13 + 3
a₆ = 16

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 6 meters so the equation becomes: 2w + 2h = 6.

Putting these two equations together and solving for width (w):

2w + 2h = 6
w + h = \( \frac{6}{2} \)
w + h = 3
w = 3 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 3 - 2w
3w = 3
w = \( \frac{3}{3} \)
w = 1

Since h = 2w that makes h = (2 x 1) = 2 and the area = h x w = 1 x 2 = 2 m²

If 44% of the town's 41,000 voters cast ballots the number of votes cast is:

(\( \frac{44}{100} \)) x 41,000 = \( \frac{1,804,000}{100} \) = 18,040

The mayor got 87% of the votes cast which is:

(\( \frac{87}{100} \)) x 18,040 = \( \frac{1,569,480}{100} \) = 15,695 votes.

The factors of a number are all positive integers that divide evenly into the number. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

First, solve for \( \left|b - 1\right| \):

\( \left|b - 1\right| \) + 7 = 0
\( \left|b - 1\right| \) = 0 - 7
\( \left|b - 1\right| \) = -7

The value inside the absolute value brackets can be either positive or negative so (b - 1) must equal - 7 or --7 for \( \left|b - 1\right| \) to equal -7:

So, b = 8 or b = -6.