# What comes next in this sequence, and why?

I'm having the hardest time with this sequence puzzle. The mobile game I play (which asked me the question) doesn't provide answers or explanations for incorrect answers, and I'm searching online so I can better understand it.

What comes next in this numeric sequence: $$5, 13, 7.5, 9.5, 10, 6, 12.5, ?$$

The multiple-choice answers provided are: $$2.5,\, 3,\, 3.5,\, 8,\, 13$$

I'm completely at a loss and would appreciate any input. Thank you!

• Hi @Dana, welcome to Puzzling SE! Take the tour if you haven't already! It's great to hear that you figured out the solution to this puzzle on your own. You do mention though in your post that this puzzle came from a mobile game. Can you provide the name of the game so that your puzzle will be properly attributed? Thanks! – HTM Dec 6 '19 at 3:05

OH MY GOD I just got it. Like, as I was looking at my own question. Boy do I feel silly.

It's a pattern for every OTHER number (5, 7.5, 10, 12.5, adding 2.5 for each sequential number); (13, 9.5, 6, subtracting 3.5 to reach each subsequent number).

The next number is

2.5 (6-3.5).

PHEW that was bugging the bejeezus out of me! Hahaha

• Glad you worked it out! Remember to come back and accept this in a couple of days' time! – F1Krazy Dec 6 '19 at 11:54
• I noticed that rot13(rirel cnve bs ahzoref fhz gb na rire qrpernfvat ahzore - 18, 17, 16, 15...) – Vilx- Dec 6 '19 at 12:24

2.5

because even terms reduce by 3.5

The sequence is two sequences interlaced. That is what makes it difficult to figure out.

The odd places in the sequence are: 5, 7.5, 10, 12.5. Each number increases by 2.5.
The even places in the sequence are: 13, 9.5, 6. Each number decreases by 3.5.
Since the next item in the sequence is at an even place, that would make it 6 - 3.5 = 2.5. So that is the answer.