The equation for this sequence is:

a_n = a_n-1 + 3(n - 1)

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(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46

The amount of flour you need is (2 - 1\(\frac{3}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{16}{8} \) - \( \frac{14}{8} \)) cups
\( \frac{2}{8} \) cups
\(\frac{1}{4}\) cups

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $100
i = 0.05 x $100
i = $5

To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{28}{80} \) = \( \frac{\frac{28}{4}}{\frac{80}{4}} \) = \( \frac{7}{20} \)

To subtract 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 11 are [11, 22, 33, 44, 55, 66, 77, 88, 99]. The first few multiples they share are [33, 66, 99] making 33 the smallest multiple 3 and 11 share.

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

\( \frac{8 x 11}{3 x 11} \) - \( \frac{4 x 3}{11 x 3} \)

\( \frac{88}{33} \) - \( \frac{12}{33} \)

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

\( \frac{88 - 12}{33} \) = \( \frac{76}{33} \) = 2\(\frac{10}{33}\)