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Which of the sequence 20,19 1/2, …

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Which of the sequence 20,19 1/2, 18 1/2, 17 3/4 is the first negative term

Posted by Hemant Sabhani 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

The given sequence is an A.P. in which first term a = 20 and common difference d = {tex}-\frac34{/tex}
Let the n^th term of the given A.P. be negative then
T_n < 0
a+(n-1)d<0
20+(n-1)({tex}-\frac34{/tex})<0
On multiplication by 4 we get
80-3n+3<0
83-3n<0
83<3n
Or 3n>83
{tex}n > \frac{83}{3}{/tex}
n > 27.67
Hence 28th term will be first negative term

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