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Determine x so that 3/5,x and 5x/3 are three consecutive terms of an ap

$G i v e n t h a t : \frac{3}{5}, x, \frac{5 x}{3} a r e t h r e e c o n \sec u t i v e t e r m s o f a n A . P . S i n c e c o m m o n d i f f e r e n c e s o f a n A . P . a r e e q u a l, t h e r e f o r e, x - \frac{3}{5} = \frac{5 x}{3} - x \Rightarrow \frac{5 x - 3}{5} = \frac{5 x - 3 x}{3} \Rightarrow \frac{5 x - 3}{5} = \frac{2 x}{3} \Rightarrow 3 (5 x - 3) = 10 x \Rightarrow 15 x - 9 = 10 x \Rightarrow 5 x = 9 \Rightarrow x = \frac{9}{5} H e n c e, x = \frac{9}{5}$

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