If $(p + 1) t h$ term of an A.P. is twice the $(q + 1) t h$ term, Prove that the $(3 p + 1) t h$ term $= m (p + 1) t h$ term.Find $m$

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Solution

$(p + 1)$ term of A.P. $= 2 [(9 + 14) t e r m] a + p d = 2 a + 22 d (3 p + 1) t e r m = m [(p + q + 1) t e r m] a + 3 p d = m [a + (p + 2 d)] 2 a + 22 d + 2 p d = m [a + (p + q) d] 2 (a + (p + q) d) = m [a + (p + q) d] m = 2$

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Similar questions

If ${(p + 1)}^{t h}$ term of an A.P is twice ${(q + 1)}^{t h}$ term, Prove that ${(3 p + 1)}^{t h}$ term is twice the ${(p + q + 1)}^{t h}$ term.

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