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# The average (arithmetic mean) of fifteen consecutive integers is 88.

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Re: The average (arithmetic mean) of fifteen consecutive integers is 88. [#permalink]
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Bunuel wrote:
The average (arithmetic mean) of fifteen consecutive integers is 88. What is the greatest of these integers?

A. 93
B. 94
C. 95
D. 96
E. 97

8th integer = 88

We need to find out 15th integer.

15 - 8 = 7.

So, 88 + 7 = 95

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Re: The average (arithmetic mean) of fifteen consecutive integers is 88. [#permalink]
Bunuel wrote:
The average (arithmetic mean) of fifteen consecutive integers is 88. What is the greatest of these integers?

A. 93
B. 94
C. 95
D. 96
E. 97

a+7= 88
a= 81
a+14 ; 81+14 = 95
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Re: The average (arithmetic mean) of fifteen consecutive integers is 88. [#permalink]
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Bunuel wrote:
The average (arithmetic mean) of fifteen consecutive integers is 88. What is the greatest of these integers?

A. 93
B. 94
C. 95
D. 96
E. 97

For consecutive integers, each increases by $$1$$ than its previous number.

So, if the First number is $$= x$$

The second number will be $$=x+1$$

The third number is = x+2, So, we see each incremental number is 1 less than its position.

So, the fifth number is $$x+14$$

The average of the consecutive number is the average of the first number and the last number.

Thus, $$\frac{x+x+14}{2}=88$$

$$2x+14=176$$

$$2x=162$$

$$x=81$$

The largest number is $$= 81+14=95$$

The answer is $$95$$
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Re: The average (arithmetic mean) of fifteen consecutive integers is 88. [#permalink]
Top Contributor
Given that The average (arithmetic mean) of fifteen consecutive integers is 88 and we need to find the greatest of these integers

============================================================

Theory
‣‣‣ In Case of consecutive number Mean = Middle term

============================================================

Let the middle term be x

=> Mean = middle term = x = 88

Now, the numbers are consecutive so the greatest or the last term will be 7 more than the middle term = x + 7 = 88 + 7 = 95