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April 11th, 2017, 02:15 AM   #1
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Working out numbers which are in both sequences.

This question's really stumped me, and I can't seem to find any tutorials on how to answer it...

The nth term of a sequence is 2n + 1
The nth term of a different sequence is 3n  1

Work out the three numbers that are
in both sequences
and
between 20 and 40

Now the three numbers I managed to get are 25, 31 and 37 (as I assumed it meant the output of both of these sequences needs to be the same as well as being in between 20 and 40). For example 2x18+1= 37 as does 3x12+1= 37.

Yet I still feel I'm going the wrong way around this.

Many thanks in advance

Last edited by skipjack; April 11th, 2017 at 04:05 AM.
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April 11th, 2017, 02:45 AM   #2
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Quote:
Originally Posted by WarmCustard View Post
This question's really stumped me, and I can't seem to find any tutorials on how to answer it...

The nth term of a sequence is 2n + 1
The nth term of a different sequence is 3n  1

Work out the three numbers that are
in both sequences
and
between 20 and 40

Now the three numbers I managed to get are 25, 31 and 37 (as I assumed it meant the output of both of these sequences needs to be the same as well as being in between 20 and 40). For example 2x18+1= 37 as does 3x12+1= 37.

Yet I still feel I'm going the wrong way around this.

Many thanks in advance
$2n+1$ will be all the odd numbers

$3n+1$ will be odd for $n$ even

the numbers with even index in the 2nd sequence between 20 and 40 are

25,31,37 as you discovered.

Last edited by skipjack; April 11th, 2017 at 04:06 AM.
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