Discussion
Which term of the progression 19, 18.2, 17.4, ... is the first negative term?
Answer: B
This is an A.P. with first term \(a=19\) and common difference \(d = 18.2 - 19 = -0.8\). We want to find the smallest n for which the nth term is less than 0. \(a_n = a + (n-1)d < 0 \Rightarrow 19 + (n-1)(-0.8) < 0 \Rightarrow 19 < 0.8(n-1) \Rightarrow 19/0.8 < n-1 \Rightarrow 23.75 < n-1 \Rightarrow 24.75 < n\). The smallest integer n satisfying this is 25. So, the 25th term is the first negative term.
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