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
Consecutive odd integers.
This topic has expert replies
- DanaJ
- Site Admin
- Posts: 2567
- Joined: Thu Jan 01, 2009 10:05 am
- Thanked: 712 times
- Followed by:550 members
- GMAT Score:770
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.
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.