Thread: Next number in a sequence.

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.

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?

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

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

Hello, RAINERI!

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

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

What is the next number after 2?

Write the numbers as fractions . . .

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


Note the pattern:

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

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

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