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We know that the sum of the smallest and the largest numbers is 114. Let's denote the smallest number as x. The consecutive odd integers can be represented as x, x+2, x+4, x+6, x+8, x+10, x+12. So, the largest number is x+12.

Given that x + (x+12) = 114
2x + 12 = 114
2x = 102
x = 51

So, the smallest number in the sequence is 51.
To find the average of a sequence of the consecutive odd integers, we can use the property that the average is the middle number in the sequence. Since we are dealing with 7 consecutive odd integers, the middle number will be the fourth number in the sequence.
So, the average will be x + 6 = 57
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Hello from the GMAT Club BumpBot!

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