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pls answer-- in an AP if a_p+1 = 2a_q+1prove that a_3p+1 = 2a_p+q+1..

$L e t a b e t h e f i r s t t e r m a n d d b e t h e c o m m o n d i f f e r e n c e o f a n A . P . G i v e n, a_{p + 1} = 2 a_{q + 1} \Rightarrow a + [(p + 1) - 1] d = 2 (a + [(q + 1) - 1] d) \Rightarrow a + p d = 2 (a + q d) A d d i n g 2 p d o n b o t h s i d e, w e h a v e, a + p d + 2 p d = 2 (a + q d) + 2 p d \Rightarrow a + 3 p d = 2 (a + (p + q) d) \Rightarrow a + [(3 p + 1) - 1] d = 2 (a + [(p + q + 1) - 1] d) \Rightarrow a_{3 p + 1} = 2 a_{p + q + 1} H e n c e p r o v e d .$

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