SOLUTION: Express the sum using summation notation. 15+13+11+...+(-43)

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Question 1059603: Express the sum using summation notation. 15+13+11+...+(-43)
Found 2 solutions by Boreal, Edwin McCravy:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
sum%2815-2n+%2CN=0%2C+30%29
This will start at 15, and 30 sums later will add -43.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Too many tutors are like the above. They show you nothing but what 
the back of the book does.  They just give you the answer with no
explanation.

Express the sum using summation notation. 15+13+11+...+(-43)
The sequence 15, 13, 11, ..., -43 is an arithmetic sequence
with a%5B1%5D=15 and since 13-15 = -2, 11-13=-2, the common
difference d=-2.

Therefore, the nth term is given by:

a%5Bn%5D%22%22=%22%22a%5B1%5D%2B%28n-1%29d

a%5Bn%5D%22%22=%22%2215%2B%28n-1%29%28-2%29

a%5Bn%5D%22%22=%22%2215-2%28n-1%29

a%5Bn%5D%22%22=%22%2215-2n%2B2

a%5Bn%5D%22%22=%22%2217-2n

Next we must find which term of the sequence is -43,
so we substitute -43 for an

-43%22%22=%22%2217-2n
-60%22%22=%22%22-2n
30%22%22=%22%22n

So the sum is

sum%28%2817-2n%29%2Cn=1%2C30%29

Edwin