Find the value of $y$ if the first three terms of an $A P$ respectively are $3 y - 1, 3 y + 5$ and $5 y + 1$ .

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Solution

$2 n d t e r m - 1 s t t e r m = 3 r d t e r m - 2 n d t e r m \Rightarrow 3 + 5 - (3 y - 11) = 5 y + 1 - (3 y + 5) \Rightarrow 3 y + 5 - 3 y + 11 = 5 y + 1 - 3 y - 5 \Rightarrow 16 = 2 y - 4 \Rightarrow 2 y = 16 + 4 \Rightarrow y = \frac{20}{2} = 10$

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