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Quadratic Equations

In a certain ...

Question

In a certain A.P. the $32^{n d}$ term is twice the $12^{t h}$ term. Then $70^{t h}$ term $= m 31^{t h}$ term. Find $m$

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Solution

Since, $32^{n d}$ term of A.P. $= 2 (1 2^{t h} t e r m)$
$a + 31 d = 2 (a + 11 d) 9 d = a 70 t h t e r m = m (31 t h t e r m) a + 69 d = m (a + 30 d) (1 - m) a = (30 m - 69) d 9 (m - 1) = 69 - 30 m 39 m = 78 m = 2$

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