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Sum of N Terms of an AP

If 2a=b+3b-...

Question

If $2 a = \frac{b + 3}{b - 1}$ and $a = 3$ , find $b$

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Solution

Given that,
$a = 3$
$2 \times 3 = \frac{b + 3}{b - 1}$
$6 (b - 1) = b + 3$
$6 b - 6 = b + 3$
$5 b = 9$
Hence,
We get $b = \frac{9}{5}$

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