Quote:
Originally Posted by Pi=
Alright, I have homework I need finished by tommorrow. Here is a problem or two.
7. Expressed in terms of n what is the sum of all the terms in the arithmetic sequence (n7), (n2), . . . . (n+428)?
8. If x = a/b, find (a+b)/(ab) in terms of x.

7. If the first term is n  7 and the second term is n  2, then I am assuming the common difference, d, is +5.
The sum, Sn, of an arithmetic progression is equal to (n/2)(a1 + an) where a1 is the 1st term and an is the nth term. So we need to find n.
an = a1 + d(n  1)
Substituting gives:
(n + 428) = (n  7) + 5(n  1)
n + 428 = n  7 + 5n  5
n + 428 = 6n  12
440 = 5n
n = 88
So n + 428 is the 88th term in the progression.
Then the sum of the 1st 88 terms in the progression, S88, is given by:
S88 = (88/2)(n  7 + n + 428)
S88 = 44(2n + 421)
S88 = 88n + 18524
Hope this helps.