### Brain Teasers

# 6, 9, 13, 16, 21, 25...

Series
Series teasers are where you try to complete the sequence of a series of letters, numbers or objects.Series

What are the next 5 numbers in this series?

6, 9, 13, 16, 21, 25...

6, 9, 13, 16, 21, 25...

### Answer

31, 34, 39, 47, 51The nth term of the series represent the sum of the nth prime number and the nth composite number

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## Comments

An easy way to look at it is by looking at the consecutive differences:

9 - 6 = 3

13-9 = 4

16-13=3

21-16= 5

25-21=3

31-25= 6

Every other sum is either 3 or it is one more than the sum 2 before it.

Hmmm well that made sense in my head anyway, sorry if it didn't really help.

Anyways, good series teaser.

9 - 6 = 3

13-9 = 4

16-13=3

21-16= 5

25-21=3

31-25= 6

Every other sum is either 3 or it is one more than the sum 2 before it.

Hmmm well that made sense in my head anyway, sorry if it didn't really help.

Anyways, good series teaser.

I got every odd term is...

6+7=13

13+8=21

and for the even terms were squares

3=9

4=16

2=25

6+7=13

13+8=21

and for the even terms were squares

3=9

4=16

2=25

I used the same reasoning as darkpaladin. At least someone else was on the same wavelength! Fun, just the same.

Erm...marching...25-21 is 4 not 3.

I'm guessing you are assuming that the 1st prime is 2, not 1. I was taught differently, but... eh.

I had something completely different. Every 2nd number being a square, and the alternate number being the square + the square root + 1.

Thus

3^2 = 9

3^2 + 3 + 1 = 13

4^2 = 16

4^2 + 4 + 1 = 21

5^2 = 25

5^2 + 5 + 1 = 31

6^2 = 36

6^2 + 6 + 1 = 43

then 49, 57, 64 and so on...

So each alternate number was

x^2 + x^1 + x^0

Of course looking back that means the first number should have been 7... missed it by that much.

Thus

3^2 = 9

3^2 + 3 + 1 = 13

4^2 = 16

4^2 + 4 + 1 = 21

5^2 = 25

5^2 + 5 + 1 = 31

6^2 = 36

6^2 + 6 + 1 = 43

then 49, 57, 64 and so on...

So each alternate number was

x^2 + x^1 + x^0

Of course looking back that means the first number should have been 7... missed it by that much.

lol lol... very nice... it's good to see the different ways that you guys were thinking this out

Whoever told you that 1 is a prime number is flat wrong. A prime number has exactly two factors, 1 and itself. The number 1 has only 1 factor: 1.

that was a good one ! you shood be proud of yourself!

Good one!

Write me!

Redangle65

Good one!

Write me!

Redangle65

udoboy, I don't know about that. Actually, I do. I just checked. You're right. But the logic is flawed. 1 is a mupltiple of only 1 and itself, because itself is one. The reason it is not included is that it is rather sadistic. It's pushing logic too far. It's pointless. It's like how everyone uses highest common factor and lowest common multiple but no one uses lowest common factor and highest common multiple because it's 1 and infinity.

rant over.

rant over.

I don't get it...............

What are the next 5 numbers in this series?

6, 9, 13, 16, 21, 25...

wat i thought was a bit different..

first of all every even spaced no. is square.. 9, 16, 25 .. so next ven places shud b occupied by 36, 49, 64...

now abt the odd places..

take 13 = 9 + sqrt(16)

21 = 16 + sqrt(25)

so the next odd spaced no shud b..

25 +sqrt(36) =31

36 +sqrt(49) = 43

49+ sqrt(64) =57...

so the series become..

6,9,13,16,21,25,31,36,43,49,57,64,....

6, 9, 13, 16, 21, 25...

wat i thought was a bit different..

first of all every even spaced no. is square.. 9, 16, 25 .. so next ven places shud b occupied by 36, 49, 64...

now abt the odd places..

take 13 = 9 + sqrt(16)

21 = 16 + sqrt(25)

so the next odd spaced no shud b..

25 +sqrt(36) =31

36 +sqrt(49) = 43

49+ sqrt(64) =57...

so the series become..

6,9,13,16,21,25,31,36,43,49,57,64,....

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