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Arithmetic Progression

If three numb...

Question

If three numbers a, b, and c are in an A.P, then which of the following is/are the arithmetic mean between a and c?

$\frac{a - c}{2}$

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$\frac{a + c}{2}$

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$\frac{a c}{2}$

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Solution

The correct options are
B
$\frac{a + c}{2}$

C
b

If three numbers a, b and c are in an A.P., then b is the arithmetic mean between a and b.

Since a, b, and c are in A.P, b - a = c - b i.e., b = $\frac{c + a}{2}$ .

Hence both option (b) and option (c) are correct.

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