how do you find the next three answer in this maths sequence 1,8,27,64 thanks?

Answer 1

125
216
343

Answer 2

You could try brute force ie working out the sequence to 40 or whatever and then counting up to the entry you need. Or you could play smart and work it out using your knowldege (I reckon u know how to do it but are just scared off by the questions and the apparent complexity). 1. The first number is 2x1, the second 2x2, the third 2x3, etc. Therefore the 40th is 2x40 = 80. The above is what I first thought, but when I re-read the question I reckon I made a mistake as they ask for the 40th digit, not the 40th number in the sequence. Therefore I think it might be like this: After 2,4,6,8 all the numbers contain two digits, eg 10,12,14,26 so lets forget 2,4,6,8 for now. Taking the first 4 numbers from the sequence leaves us a further 36 places to go to get to the 40th position. So pretend we need the 36th digit and that 10 is the first number in the sequence taking up two places with its two digits, ie 1 and 0 are at places 1 and 2 in the sequence. Because each number takes 2 places then we half 36 to get 18. Then we add the original four we took off at the start to get 22. Therefore, contrary to my original answer we need the second digit of the number at the 22nd postion ie second digit of 44 which is of course 4. 2. OK lets give the colours numbers according to their place in the sequence: Orange=1 Red=2 Green=3 Yellow=4 Gray=5 The first square is blue and then not used again so forget that one using the other colours and one less square: Now we can work it out using maths again: 96/5=19 remainder one. Therefore 95 would be Gray and therefore the extra 1 ie 96 would be Orange. This would actually be 97 as we forgot the first square, remember? 3. Similar question again: There are 3 numbers in the sequence that then repeats itself. 2 is at place 1,4,7 etc ie every 3 after the first place. The same for the other two numbers ie 5 is at place 2,5,8 etc and 7 is at 3,6,9,12 etc. Therefore we use division again to work this out: 12/3=4, no remainder, therfore the 12th place in the sequence is held by number 7 as 7 is the last one in the three number sequence. 91/3=30 remainder 1. If there were no remainde rthen the answer would be 7 again, but it is one further on than that so the next number is 2. Therefore the 91st number is 2. They want the answer to 12th + 91st = 7 + 2 = 9. 4. OK there are 5 terms in the original sequence that then repeats itself. They want 20 terms in the sequence so there are 20/5=4 full sequences of the above sequence (if that makes any sense). They want the product of the first 20 terms. The first 5 terms gives us -1 x 2 x 3 x 1 x 0.5 = -3. We need four of these so -3 x -3 x -3 x -3 = 81. I hope this has been of some help and that I haven't made any mistakes. Good luck and sorry if I haven't made my workings clear enough but hope I have given you something to get you going in the right direction. PS as you can see a lot of people on here have made mistakes due to not reading the question properly initially (myself included, however I think they are corrected). Take note - always read the question properly and at least twice. Then try to work out exactly what it is they are asking you to do. I should take that advice also, lol.

Answer 3

The trick (and the reason to learn about this in math classes) is to be able to reason your way through this problem, instead of blindly trying things out on a calculator.

In this case, for people who see the ratio behind this sequence, it jumps at them (and they have provided you with the answer).

Sequences often follow arthmetical rules or geometrical rules (and there are many other kinds of rules, but those come later).

The first thing to try, normally, is differences: Find the difference between each number (tis creates a new sequence) and see if you can break that sequence.

Here, the differences are: 7, 19, 37.
Differences of differences: 12, 18.

Looks like the difference of differences grows by 6 at every step, so that the next "diff-or-diff" could be: 24, 30, 36...
Applying them to differences, we get:
37+24 = 61
61+30 = 91
91+36 = 127

Let us apply these differences to the original sequence:
64 + 61 = 125
125 + 91 = 216
216 + 127 = 343

We can extend the sequence as far as we want (using the difference-of-differences method) even if we had failed to guess that it was a list of cubes.

There is a link between the fact that the third differential of a cube is a constant (in calculus) and the fact that our third level -- difference of differences of differences is also a constant (6). This trick was known to Isaac Newton and was used by Indian mathematicians in the 8th century.

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In other sequences, if the differences don't help you, try ratios. In this case, the ratios are 8, 3.375, 2.3703704 and they do not help us. However, in a geometric sequence, ratios could have helped.

Answer 4

The pattern is 1³, 2³. 3³, 4³, ... .
So the next 3 numbers are 5³ = 125, 6³ = 216 and
7³ = 343.

Answer 5

Its its N to the 3rd power

So 1^3 = 1
So 2^3 = 8
So 3^3 = 27
So 4^3 = 64
So 5^3 = 125
So 6^3 = 216
So 7^3 = 343

Answer 6

its 125 or 5*5*5
then 216 or 6*6*6
then 343 or 7*7*7

An easy way to see all of your cubes is to graph y=x^3 in your calculator and hit 2nd graph to see the table.

x: y:
1 1
2 8
3 27
4 64
5 125
6 216
7 343
8 512
9 729
10 1000

Answer 7

3
n = n*n*n
1*1*1 = 1
2*2*2 = 8
3*3*3 = 27
4 *4*4 = 64
now the next 3 numbers would be
5*5*5=125
6*6*6= 216
7*7*7=343

the next sequence is 1,8,27,64,125,216,343

Answer 8

1 cubed = 1
2 cubed = 8
3 cubed = 27
4 cubed = 64
you need 5, 6 and 7 cubed

125, 216, 343

Answer 9

ok these are cube numbers

1*1*1=1
2*2*2=8
3*3*3=27
4*4*4=64
5*5*5=125
6*6*6= 216
7*7*7=343

Answer 10

125, 216, 343

Answer 11

125, 216, 343