If (3y-1), (3y+5), and (5y+1) are three consecutive terms of an AP then find the value of y from the option given below.

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answer is C.

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Detailed Solution

It is given that (3y-1), (3y+5), and (5y+1) are in AP.
From the given information,

a 1 = 3 y − 1, a 2 = 3 y + 5, a 3 = 5 y + 1

We have to find the value of y.
The consecutive terms have the same common difference. So,

a 2 − a 1 = a 3 − a 2

Substitute the known values in the formula,

(3 y + 5) − (3 y − 1) = (5 y + 1) − (3 y + 5)

3 y + 5 − 3 y + 1 = 5 y + 1 − 3 y − 5

2 y = 6 + 4

2 y = 10

y = 5

The value of y is 5.
Hence, option 3) is correct.

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