Next number in a sequence.

**RAINERI** · Nov 25th 2010, 07:52 AM

Hello. This must be a silly question I guess but I have been trying to solve this but I simply cannot find any formula, so please someone help. Thank you.

1,2
1,25
1,3333333333333333333333333333333
1,5
2
x <------ so what is the next number after 2? Can you please also include the formula so I know how it is calculated? Thank you very much.

**Unknown008** · Nov 25th 2010, 08:01 AM

Look by what number the first term is multiplied to to get teh second term and so on.

You get first term times 25/24
Second term times 16/15
Third times 9/8
Fourth times 4/3

Can you find the pattern?

**RAINERI** · Nov 25th 2010, 08:32 AM

I get Fifth times 1/0 (to get the sixth number) but I cannot devide with 0 ???

**Unknown008** · Nov 25th 2010, 08:33 AM

Yes, I got the same problem. I guess that it's infinity...

**Soroban** · Nov 25th 2010, 05:03 PM

Hello, RAINERI!

I agree . . . The answer is $\dfrac{1}{0}$ . . . undefined.

. . $\begin{array}{c}1.2 \\ 1.25 \\ 1.\overline{3} \\ 1.5 \\ 2 \\ ? \end{array}$

What is the next number after 2?

Write the numbers as fractions . . .

. . $\begin{array}{ccc} 1.2 &=& \dfrac{6}{5} \\ \\[-3mm] 1.25 &=& \dfrac{5}{4} \\ \\[-3mm]1.\overline{3} &=& \dfrac{4}{3} \\ \\[-3mm]1.5 &=& \dfrac{3}{2} \\ \\[-3mm] 2 &=& \dfrac{2}{1} \end{array}$

Note the pattern:

. . $\displaystyle \frac{6}{5} \;\to\;\frac{5}{4}\;\to\;\frac{4}{3} \;\to\;\frac{3}{2} \;\to\;\frac{2}{1} \;\to\;?$

The numerators are decreasing-by-one.
The denominators are decreasing-by-one.

The next fraction must be $\dfrac{1}{0}$

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