One way that a company can raise money for expansion is to sell stock. when you buy a share of a company's stock, you become a shareholder, or part owner, of that company. the cost of a share is often represented in points, where each points represents one dollar. when a stock gains points, its shares increase in value, and when a stock loses points, its shares decrease in value. for instance, if a stock gains three points one day, each share of its stock is worth three dollars more than it was the day before. positive decimal numbers are used to represent gains, and negative decimal numbers are used to represent losses. on monday, the closing value of a share of stock in company abc, was 74.01. on tuesday, it closed at 73.67, and on wednesday, it closed at 74.32. on thursday, the change in stock value was -1.48. and, on friday, company abc's stock gained 0.89 points. answer the following questions based on company abc's stock performance this week. if on friday, a shareholder experienced a total stock value change of $42.72, how many shares of this stock do they own? shares.

change of stock price/initial stock price on friday * total stock value = change of stock value

0.89/73.73 *x = 42.72

x=3539.04 = total stock value at initial stock price on friday .

total stock value at initial stock price on friday/ initial stock price on friday = number of shares

3539.04/73.73 = 48 shares

they own 48 shares of this stock

In any artihmetic sequence, consecutive terms differ by a fixed constant c. So given the first term a, the second term is a + c, the third terms is a + 2c, and so on, up to the n-th term a + (n - 1)c.

If the 15th term is 40, then

40 = -12 + (15 - 1) c   ==>   c = 52/14 = 26/7

We can then write the n-th term as

-12 + (n - 1) 26/7 = (26n - 110)/7

The sum of the first 15 terms is then

Another way to compute the sum: let S denote the sum,

S = -12 - 58/7 - 32/7 + … + 228/7 + 254/7 + 40

Reverse the order of terms:

S* = 40 + 254/7 + 228/7 + … - 32/7 - 58/7 - 12

Notice that adding up terms in the same position gives the same result,

-12 + 40 = 28

-58/7 + 254/7 = 28

-32/7 + 228/7 = 28

so that

S + S* = 2S = 28 + 28 + 28 + … + 28 + 28 + 28

There are 15 terms in the sum, so

2S = 15×28   ==>   S = 15×28/2 = 210