First slide

Arithmetic progression

Question

If the sum of three numbers in A.P. is 24 and their product is 440, then common difference of the
A.P. can be

Moderate

A

3
B

2
C

5
D

-5

Solution

Let the three number in A.P. be $a - d, a, a + d .$
Then
$\begin{array}{l} 24 = (a - d) + a + (a + d) = 3 a \\ \Rightarrow a = 8 \end{array}$
Also, $440 = (a - d) a (a + d) = 8 (64 - d^{2})$
$\begin{array}{ll} \Rightarrow d^{2} = 64 - 55 = 9 \Rightarrow d = \pm 3 . \end{array}$
$∴ d$ can be 3.

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