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One - One function

The 19thter...

Question

The $19^{t h}$ term of An A.P. is equal to three times its sixth term.If its $9^{t h}$ term is 19 feb the A.P.

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Solution

$a_{19} = 3 a_{6} a_{9} = 19 a + 18 d = 3 (a + 5 d) a + 18 d = 3 a + 15 d 2 a - 3 d = 0 2 a = 3 d, a = \frac{3}{2} d a + 8 d = 19 \frac{3}{2} d + 8 d = 19 19 d = 38 d = 2 a = 3 ∴ 3, 5, 7, 9, . . . .$

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