For a sequence of seven integers, the difference between the largest and the smallest numbers is 14 and the arithmetic mean of the seven integers is 26. What is the greatest possible value of the largest number of the sequence?

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Explanation

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Official Explanation

Official

Let the seven integers in increasing order be:

a < b < c < d < e < f < g

Thus,

g - a = 14

a + b + c + d + e + f + g = 182

(As the arithmetic mean of these seven integers is 26)

The best way to solve such questions is to check using options.

Let's consider the greatest possible value of

g = 38

given in the options (Option E).

As

g = 38

a = g - 14 = 24

…

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What this question tests

What it tests

Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.

Common trap

Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.