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10-29-2011   #1
Pi=
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Urgent, Help

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 (n-7), (n-2), . . . . (n+428)?
8. If x = a/b, find (a+b)/(a-b) in terms of x.
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 10-29-2011 #2 Mr. Hui Last Achievements     Join Date: Mar 2005 Posts: 10,650 8. x = a/b a = bx (a+b)/(a-b) = (bx+b)/(bx-b) = (b)(x+1)/(b)(x-1) =(x+1)/(x-1) __________________ Do Math and you can do Anything!
10-29-2011   #3
MAS1

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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 (n-7), (n-2), . . . . (n+428)? 8. If x = a/b, find (a+b)/(a-b) 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.

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