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Fun With Numbers: Sequences *October 18, 2010*

*Posted by nrhatch in People.*

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Math has logic and certainty behind it.

When you see the pattern, you can predict the next step in the progression.

It’s Black & White, without the endless shades of gray that predominate elsewhere in life.

Craving a bit of logical certainty?

Here are a few easy sequences to put order back into your day:

1) 1 4 9 16 25 36 ___ ___ 81

2) 3 5 8 13 21 ___ ___ 89 144

3) 8 ___ 64 125 216 343 ___

4) 3 6 10 ___ 21 28 ___ 45 55

5) 2 4 8 16 32 ___ 128 256 ___

6) 1 4 7 10 13 ___ 19 22 ____

7) 3 9 27 81 243 ___ 2187 ____

*Answers tomorrow. *

*NOTE: Some answers may appear in the comments. Don’t scroll down until you’ve solved the sequences . . . or have given up due to lack of sleep, lack of coffee, or lack of interest. Cheers! *

Related posts: Your Role Model * The Laugh Calculator * Certainty and Symmetry * Attitude is Everything * SPOOKY: Last post = DCLXVI (666)

## Comments

Sorry comments are closed for this entry

1) 49, 64

2) 34, 55

…….

Excellent start, James . . .

You’ve got to be kidding … after being up half the night I can’t even think straight …

You are excused.

Besides, the bunny would probably eat your homework anyway. Bunnies eat everything!

The only one I can’t get is no. 3. Don’t see pattern, —YET!

Hey LL!

Glad to see you’re still popping in from time to time. 🙂

Good luck with #3.

I am with Loreen – stumped by #3.

Number 3 is the least obvious. Glad that you solved the others.

Should we write our answers down here or what?

I’m itching to do it!

*#*

You can post them here if you want. I’ll post a note above that some answers appear below.

The answers will be posted tomorrow at 8 am.

OK, I have asked permission and now, here are my answers, I don’t know how many (if any) are correct but –

1) 49 ; 64

2) 34 ; 55

3) 27

4) 15 ; 36

5) 64 ; 512

6) 16 ; 25

7) 729 ; 6561

Well, that’s that.

I cannot wait until the morning!

*#*

Hey, you should work with numbers for a living!

Oh, wait, you do. 😉

On #3, there is an empty spot at the end of the sequence you haven’t filled in. But we both know you could. Cheers!

Would 413 be a candidate with the sequence, adding up the numbers in one given figure, in order, 8, 27(9) 64(10) etc. This would mean that there are alternative possibilities, except the sequence has to increase by the ration of l0 from number to number. i.e. 0-10; 10-100; l00-200 etc. Hope I have it. That’s my submission anyway….

Interesting pattern, LL

8 = 8

2+7 = 9

6+4 = 10

1+2+5 = 8

2+1+6 = 9

3+4+3 = 10

4+1+3 = 8

I hadn’t looked at it that way. And there is another solution.

Then it is the square root(?), first of 2 (2x2x2) then of 3 (3x3x3) etc. Gonna give up writing and get into math. grin grin. Thanks for the hint…

So the answer is 512, which incidentally adds up to the magic number 8. Now why is that? I’ll bet a pure mathematician would want to know why. Don’t you?

That’s don’t you think so too!!!! Ah! language.

Not the square root, or the square, but the cube:

2 = the square root of 4 and the cube root of 8

4 = 2 squared (or 2 to the 2nd power)

8 = 2 cubed (or 2 to the 3rd power)

And, LOL, LL at “Don’t you?” I expect that mathematician would know. But I don’t. 🙂

ACK! My addiction. I won’t even look at it. It will take me to my logic problems or my sudokus and I’ll kiss the world goodbye.

I understand completely. Addictions are tough despite strong will power. 🙂

Nancy,

This is great.

In exercise #3, is it possible to be 27 and 1000?

Why 1000?

OK: I finally got around to doing this. Here are my provisional answers:

1)49; 64

2)43; 55

3)18; 413

4)15; 36

5)64; 512

6)16; 25

I say provisional because while I think I understand the pattern in each, it’s highly possible with my one hand I’ve made a typo, and I’m in too much of a hurry to go back and check it! How’s that for an excuse for a wrong answer? 😀

7)729; 2187; 6561

Well, you got some right . . . and some wrong.

OMG!!!

How could I miss that Nancy!!

3) 27 ; 512

There.

*#*

So where are the answers??!!

Oh, ahem, it’s not 8 am yet.

DAMN IT!! It’s just after midnight!

Oh the torture!

I guess you can see I absolutely LOVE numbers, right?

*#*

I do too! I’m going to have to find some new stuff for Fun with Numbers.

49 64 square of no.s

34 55 previous no. + later no.

27 512 cubes

15 36 +3,+4,+5

64 512 *2

16 25 +3

729 6561 *3

Well done, humm! A perfect “10”!

I’ll see what other math puzzle I can find to challenge you all with.

Nan,

This is quite fun!

Why 1000?

Every even number will follow a pattern of cubed 2 multiplied per cubed n where n is the place of the even number in the series.

Every odd number will follow a pattern of cubed prime number starting at 3.

8 = 2^3 x 1^3 27 = 3^3

64 = 2^3 x 2^3 125 = 5^3

216 = 2^3 x 3^3 343 = 7^3

1000 = 2^3 x 4^3 1331 = 11^3

Your explanation got caught in the Spam Filter. Guess WP didn’t like the look of all those numbers.

Interesting pattern but if I follow your lead, the answer is still 512, not 1000:

2x2x2= 8

4x4x4=64

8×64=512

You’re right, Nancy.

My bad. Sorry.

The place in the series for the even numbers that correspond to a prime number…

So the fourth term should be cubed two times cubed five equals a thousand.

Gotcha! Your solution works . . . and I wouldn’t have thought of it on my own. Nice job.