SOLUTION: Sum -(in summation notation) lower limit is i = 3 and upper limit is n of: (-3-4i) = -507 Find the value of n.

Algebra ->  Sequences-and-series -> SOLUTION: Sum -(in summation notation) lower limit is i = 3 and upper limit is n of: (-3-4i) = -507 Find the value of n.      Log On


   

Question 849495: Sum -(in summation notation)
lower limit is i = 3 and upper limit is n of:
(-3-4i) = -507
Find the value of n.
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
sum%28%28-3-4i%29%2Ci=3%2Cn%29

That's the sequence

-3-4(3) = -3-12 = -15
-3-4(4) = -3-16 = -19
-3-4(5) = -3-20 = -23
-3-4(6) = -3-24 = -27
...
-3-4(n) = -3-4n

So that is the sum of the arithmetic sequence with
first term -15, last term -3-4n and n-2 terms [there are
2 less since are no terms for i=1 or i=2]

Sum = expr%28%28number_of_terms%29%2F2%29%28first_term%2Blast_term%29

Sum = expr%28%28n-2%29%2F2%29%28-15%2B%28-3-4n%29%29

Sum = expr%28%28n-2%29%2F2%29%28-15-3-4n%29

Sum = expr%28%28n-2%29%2F2%29%28-18-4n%29%29

Sum = expr%28%28n-2%29%2F2%29%28-2%29%289%2B2n%29%29

Sum = expr%28%28n-2%29%2Fcross%282%29%29%28-cross%282%29%29%289%2B2n%29%29

Sum = -%28n-2%29%289%2B2n%29%29

Edwin

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
I changed my solution:

sum%28%28-3-4i%29%2Ci=3%2Cn%29

That's the sequence

-3-4(3) = -3-12 = -15
-3-4(4) = -3-16 = -19
-3-4(5) = -3-20 = -23
-3-4(6) = -3-24 = -27
...
-3-4(n) = -3-4n

So that is the sum of the arithmetic sequence with
first term -15, last term -3-4n and n-2 terms [there are
2 less since are no terms for i=1 or i=2]

Sum = expr%28%28number_of_terms%29%2F2%29%28first_term%2Blast_term%29

Sum = expr%28%28n-2%29%2F2%29%28-15%2B%28-3-4n%29%29

Sum = expr%28%28n-2%29%2F2%29%28-15-3-4n%29

Sum = expr%28%28n-2%29%2F2%29%28-18-4n%29%29

Sum = expr%28%28n-2%29%2F2%29%28-2%29%289%2B2n%29%29

Sum = expr%28%28n-2%29%2Fcross%282%29%29%28-cross%282%29%29%289%2B2n%29%29

Sum = -%28n-2%29%289%2B2n%29%29

Edwin