Sequences

guest_need_help · 2006-09-13 06:24:42

can anyone tell me how you work out the nth term please

1/2 2/5 3/8 4/11 5/14

Dross · 2006-09-13 06:59:50

guest_need_help wrote:

can anyone tell me how you work out the nth term please
1/2 2/5 3/8 4/11 5/14

What this question is aksing about is pattern spotting. One way to look at it is to consider the numbers in the top of the fractions (ie the numerators) seperately from the numbers in the bottom halves of the fractions (ie the denominators).

So in the sequence:

split the numerators and denominators into two "rows" of numbers (they actually aren't, but we can think of them as two rows of numbers to help us solve the problem) and have a look along the top row, decide how those numbers are progressing, then along the bottom row to decide how those numbers are progressing. Looking at the top row only, the numbers go:

1, 2, 3, 4, 5...

So the numbers each time are increacing by 1. Looking at the bottom row of numbers:

2, 5, 8, 11, 14...

The numbers each time are increacing by 3.

So we can see that the next few terms would turn out to be:

Now we have to give an expression for the nth term, which we can do because we know how the pattern goes. In this case, we can find a formula for the nth numerator, a formula for the nth denominator, and combine them to find a formula for the nth term.

So, the pattern for the numerators shows that the formula for the nth denominator is simply n.

Looking at the pattern for the denominators, the nth denominator must be given by 3n - 1. (the 3n appears because the terms increace by 3 each time, the - 1 term tagged on the end appears because the first denominator is 2)

So, we now have to combine these to get our formula for the nth term:

guest_need_help · 2006-09-13 07:10:47

wow you are very good at explaining it clear thank you

Dross · 2006-09-14 02:20:33

guest_need_help wrote:

wow you are very good at explaining it clear thank you

Glad to have been able to help!

Math Is Fun Forum

#1 2006-09-13 06:24:42

Sequences

#2 2006-09-13 06:59:50

Re: Sequences

#3 2006-09-13 07:10:47

Re: Sequences

#4 2006-09-14 02:20:33

Re: Sequences

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