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Umnica [9.8K]
2 years ago
9

The average of a set of 18 consecutive integers is 22.5. what is the smallest integer in the set?

Mathematics
1 answer:
quester [9]2 years ago
6 0
The sum of the 18 numbers is 22.5 x 18 = 405.
Let the numbers be x, x + 1, x + 2, . . ., x + 17

Sum of n term of an arithmetic sequence = n/2(a + l)
18/2(x + x + 17) = 405
9(2x + 17) = 405
2x + 17 = 405/9 = 45
2x = 45 - 17 = 28
x = 28/2 = 14

Therefore, the smallest integer is 14.
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