The equation for this sequence is:

a_n = a_n-1 + 2

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 + 2
a₆ = 9 + 2
a₆ = 11

40% of the water consumption is industrial use and 14% is personal use so (40% - 14%) = 26% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{26}{100} \) x 35,000 gallons = 9,100 gallons.

The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 6 have in common.

The factors of 44 are [1, 2, 4, 11, 22, 44] and the factors of 28 are [1, 2, 4, 7, 14, 28]. They share 3 factors [1, 2, 4] making 4 the greatest factor 44 and 28 have in common.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 3}{3 x 3} \) + \( \frac{4 x 1}{9 x 1} \)

\( \frac{12}{9} \) + \( \frac{4}{9} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{12 + 4}{9} \) = \( \frac{16}{9} \) = 1\(\frac{7}{9}\)