which term of sequence,24,23 1/4,22 1/2,21 3/4 is the first negative term?

Asked by  | 17th Apr, 2009, 06:09: PM

Expert Answer:

Since the given sequence has values that go on decreasing, so there are two choices.

Either the term zero appears in the sequence at some stage or it doesn't.

If it appears, then the term after that will be the first negative term.

If zero is not a term of this sequaence then the first negative term will come after the last positive term.

Suppose we put the nth term as zero, then if zero is actually a term of this sequence, then n will come out as an integer value.

If not, it will come as a fraction value.suppose we get n as 3.5, then we can say that 3rd term is the last positive term.So then 4th term is the first negative term.

Now that we have fixed the method,let's proceed.

For the given sequaence,

first term = a= 24

 common diff= d= -0.75

So nth term =a+(n-1)d=24+(n-1)(-0.75)=24.75-[(0.75)*(n)]

So putting the nth term equal to zero, we get,

n=33

So this being an integral value, we see that the 33rd term is equal to zero, so naturally the term after that must be the first negative term.

So 34th  term is the first negative term.-

note

It can be checked that the 34th term

=a+33d

=24+[33*(-0.75)]

= -0.75 is a negative value.

 

 

Answered by  | 24th Apr, 2009, 09:02: AM

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