# Average of 9 consecutive integers is 50. Find the sum of largest and smallest integers.

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Average of 9 consecutive integers is 50. Find the sum of largest and smallest integers.
1. 110
2. 54
3. 100
4. 46

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Correct Answer - Option 3 : 100

Given:

Average of 9 consecutive integers is 50.

Concepts used:

Average = (Sum of all observations)/(Number of observations)

Calculation:

Let first intger be x.

So, nine consecutive numbers are x, (x + 1), (x + 2), (x + 3), (x + 4), (x + 5), (x + 6), (x + 7) and (x + 8)

Sum of 9 consecutive integers = x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) + (x + 7) + (x + 8) = 9x + 36

Average = Sum of all observations/Number of observations

⇒ 50 = (9x + 36)/9

⇒ x + 4 = 50

⇒ x = 50 – 4 = 46

Smallest integer = x = 46

Largest integer = x + 8 = 46 + 8 = 54

Sum of largest and smallest integers = 46 + 54 = 100

∴ The sum of largest and smallest integers is 100.

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