SOLUTION: Determine the sum of the first 1000 multiples of 5. (please show equation) 2. in how many ways can nine people be selected from group of 10

Question 902708: Determine the sum of the first 1000 multiples of 5. (please show equation)

2. in how many ways can nine people be selected from group of 10
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
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

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