The equation for this sequence is:

a_n = a_n-1 + 4(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 + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

If the tiger has consumed 96 pounds of food in 8 days that's \( \frac{96}{8} \) = 12 pounds of food per day. The tiger needs to consume 156 - 96 = 60 more pounds of food to reach 156 pounds total. At 12 pounds of food per day that's \( \frac{60}{12} \) = 5 more days.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

6x⁶ - 4x⁶
(6 - 4)x⁶
2x⁶

42% of the water consumption is industrial use and 25% is personal use so (42% - 25%) = 17% more water is used for industrial purposes. 15,000 gallons are consumed daily so industry consumes \( \frac{17}{100} \) x 15,000 gallons = 2,550 gallons.

If 60% of the town's 19,000 voters cast ballots the number of votes cast is:

(\( \frac{60}{100} \)) x 19,000 = \( \frac{1,140,000}{100} \) = 11,400

The mayor got 78% of the votes cast which is:

(\( \frac{78}{100} \)) x 11,400 = \( \frac{889,200}{100} \) = 8,892 votes.