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

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{45mi}{15mph} \)
3 hours

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{9}{36}} \)
\( \frac{\sqrt{9}}{\sqrt{36}} \)
\( \frac{\sqrt{3^2}}{\sqrt{6^2}} \)
\(\frac{1}{2}\)

If the tiger has consumed 30 pounds of food in 5 days that's \( \frac{30}{5} \) = 6 pounds of food per day. The tiger needs to consume 54 - 30 = 24 more pounds of food to reach 54 pounds total. At 6 pounds of food per day that's \( \frac{24}{6} \) = 4 more days.