# IBM PAT Number Sequence

I am looking at an old IBM PAT (circa 1965) and am stumped by a number sequence question. This is it:

Identify the pattern in the following sequences and select the option which indicates the next element in the sequence.

6 10 7 14 14 18

• a) 14
• b) 15
• c) 16
• d) 18
• e) 21

If anyone can identify the pattern and the correct answer, I would be very interested to hear.

I believe the correct answer is b) because:

6 + 4 = 10
10 - 3 = 7
7 * 2 = 14
14 / 1 = 14
14 + 4 = 18
18 - 3 = 15

So the sequence is:

First add 4 then subtract 3 after that multiply with 2 and divide by 1

• I think I understand but some people might not. Could you please add what that sequence is? Mar 11 '19 at 13:45
• At first this answer seemed like a stretch to me, but the more I look at it, the more is makes sense. Even though there are four different steps before they begin repeating, the steps use the four basic operations in the canonical order, and the other numbers involved also have a simple pattern to them. Very clever. Mar 11 '19 at 14:49

I saw this as a merge of two series, and agree with @Coder97 about the answer being b) with different reasoning. I saw the odd indexed elements of the series following this pattern:

next = current + 1 (if even), next = current * 2 (if odd)

and the even indexed elements of the series following this pattern:

next = current + 4

It might be interesting to try and prove @Coder97 and my solutions are mathematically the same.

• Your odd-index rule matches the other solution indefinitely, but your even-index rule differs as soon as you extend the sequence to the next number. Mar 11 '19 at 23:45
• @JaapScherphuis yeah! Found that after right after I posted. Now I'm curious who designed this... Mar 12 '19 at 14:36