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nth Term of A.P

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Question

Find the first negative term of the arithmetic progression $19, 18 \frac{1}{5}, 17 \frac{2}{5}$

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Solution

$\begin{matrix} T h e t e r m i s n e g a t i v e t h e n i t s h a l l b e O > a n i n t h e f o r m a = 19 d = - 4 / 5 a n < 0 a + (n - 1) d < 0 19 + (n - 1) - 4 / 5 < 0 19 - 4 n / 5 + 4 / 5 < 0 (95 - 4 n + 4) / 5 < 0 99 - 4 n < 0 99 < 4 n 23 \frac{3}{4} < n 24 = n \end{matrix}$

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