Question

2. An auditorium has 20 seats on the first row, 24 seats on the second row, 28 seats on the third row, and so on and has 30 rows of seats. How many seats are in the theatre?

3. Suppose you go to work for a company that pays one penny on the first day, 2 cents on the second day, 4 cents on the third day and so on. If the daily wage keeps doubling, what will your total income be for working 31 days?

Answer 1

2. The formula says that the sum of the first n terms of our arithmetic sequence is equal to n divided by 2 times the sum of twice the beginning term, a, and the product of d, the common difference, and n minus 1.

$Sum = 30/2×(2×20 + (30 - 1)×4) = 2,340.$

3. The sum of these geometric sequence is

$S = \frac{1×(2^{31} - 1) } {2 - 1} = 2,147,483,647$ cents or $21,474,836.47.