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Arithmetic Mean

If 3x, 5x+1...

Question

If $3 x, 5 x + 1$ and $8 x - 1$ are in $A . P$ , then the value of $x$ is

A

2

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B

- 3

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C

- 4

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D

3

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Solution

The correct option is D $3$
Given: $3 x, 5 x + 1, 8 x - 1$ are in AP.
We know if $a, b, c$ are in A.P. then $b - a = b - c$ or $2 b = a + c$
$∴ 2 (5 x + 1) = 3 x + 8 x - 1$
$∴ 10 x + 2 = 11 x - 1$
$∴ 11 x - 10 x = 2 + 1$
$∴ x = 3$

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