Divisible by what?

Number Theory Level 3

Find the next number in the series.

2, 6, 12, 30, 42, 72

Notes: What's the title again?

You can also try this or My Other Problems .

84 96 78 90

Astro Enthusiast by Astro Enthusiast , 24, Philippines

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4 solutions

Jaydee Lucero
Aug 6, 2014

All of these numbers are products or two consecutive positive integers. 2 = 1 x 2, 6 = 2 x 3, 12 = 3 x 4, 30 = 5 x 6, 42 = 6 x 7, 72 = 8 x 9. From the given choices, only 90 has this property, since 90 = 9 x 10.

6 Helpful 0 Interesting 0 Brilliant 0 Confused

30=4*5 how it's possible

vivek kumar - 6 years, 10 months ago

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Oh, sorry, typo error. (>.<) Thanks for noticing the error. :)

Jaydee Lucero - 6 years, 9 months ago

It should be remembered that answers divisible by 6 are mentioned

Sualeh Asif - 6 years, 8 months ago
Hansraj Sharma
Jul 19, 2014

1^2+1=2 2^2+2=6 3^2+3=12 5^2+5=30 6^2+6=42 8^2+8=72 9^2+9=90

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Only that I omitted answers that aren't divisible by 6. So you can't see, 4^2+4 nor 7^2+7 :D

Astro Enthusiast - 6 years, 10 months ago
Bob Kadylo
Feb 18, 2018

See: OEIS A024701

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Azhar T
Sep 28, 2014

2x3=6,3x4=12,5x6=30.6x7=42.8x9=72,9x10=90

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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