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Question

Which term of the sequence 20,1914,1812,1734,..... is the first negative term?

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Solution

The given sequence is an A.P. in which first term (a=20) and common difference (d=34).


Let the nth term of the given A.P. be the first negative term.

Then, an<0

a+(n1)d<0

20+(n1)×(34)<0

203(n1)4<0

203n34<0

803n+34<0

833n4<0

833n<0

83<3n

3n>83

n>2723

n28[n is a natural number]

Thus 28th term of the given sequence is the first negative term.


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