Question 902708
1) the formula for the sum of an arithmetic series is:

Sn = (n/2) * (a1 + an)

Sn = the sum of the n terms in the sequence.
a1 = the first term in the sequence.
an = the nth term in the sequence.

our first term is 5 and our last term is 5000.

the common difference is 5.

to find the last term, we take the last term and divide it by 5 to get 1000.  that is, x / 5 = 1000 and x = 5000 the last term

there are 1000 terms in the sequence, so n = 1000

our formula becomes Sn = (1000/2 * (5 + 5000) which becomes (1000/2) * 5005 which becomes 500 * 5005 which becomes 2,502,500.

2) we are asked in how many ways can nine people be selected from group of 10

this is a combination (10C9) of 10 people taken 9 at a time

(10C9) = 10! / 9! * (10-9)! = 10 combinations