The number of students taking German or Spanish is 8 + 8 = 16. Of that group of 16, 5 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 16 - 5 = 11 who are taking at least one language. 18 - 11 = 7 students who are not taking either language.

To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{36}{68} \) = \( \frac{\frac{36}{4}}{\frac{68}{4}} \) = \( \frac{9}{17} \)

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] 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 [45, 90] making 45 the smallest multiple 5 and 9 share.

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

\( \frac{7 x 9}{5 x 9} \) + \( \frac{5 x 5}{9 x 5} \)

\( \frac{63}{45} \) + \( \frac{25}{45} \)

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

\( \frac{63 + 25}{45} \) = \( \frac{88}{45} \) = 1\(\frac{43}{45}\)

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

If the tiger has consumed 168 pounds of food in 12 days that's \( \frac{168}{12} \) = 14 pounds of food per day. The tiger needs to consume 210 - 168 = 42 more pounds of food to reach 210 pounds total. At 14 pounds of food per day that's \( \frac{42}{14} \) = 3 more days.