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Consecutive odd integers.

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by ramonsa » Sat Jun 06, 2009 5:14 am
Hi - Can someone explain me the approach to this problem? I'm getting 32 as an answer but I want to make sure that I using the best approach.

Thanks

3-13.If a sequence of 8 consecutive odd integers with increasing values has 9 as its 7th term, what is the sum of the terms of the sequence?
(A) 22 (B) 32 (C) 36
(D) 40 (E) 44
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by DanaJ » Sat Jun 06, 2009 6:01 am
Let a be the smallest of the 8 consecutive odd integers. This means that the second term will be a + 2, the third term will be a + 4 = a + 2*2, the fourth term will be a + 6 = a + 3*2.

Notice then that there's a certain pattern to the numbers: the nth number will be a + (n-1)*2. This makes your 7th term a + (7-1)*2 = a + 12 = 9. In this case, a will be 9 - 12 = -3. So your numbers will be:

-3, -1, 1, 3, 5, 7, 9, 11

As you can see, the first four term cancel each other out, so the sum you're looking for will be 5 + 7 + 9 + 11 = 12 + 20 = 32.
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