The next number in the series 3, 6, 4, 7, 5, 8 is 6.

Spotting the pattern

Look at how the numbers change step by step:

  • From 3 to 6: add 3
  • From 6 to 4: subtract 2
  • From 4 to 7: add 3
  • From 7 to 5: subtract 2
  • From 5 to 8: add 3

So the rule is:

Add 3, then subtract 2, and repeat.

Applying the rule

Continuing the same pattern after 5 → 8 (add 3):

  • Next step should be: subtract 2
  • 8−2=68-2=68−2=6

So the next number that fits the alternating pattern of +3,−2,+3,−2,…+3,-2,+3,-2,\dots +3,−2,+3,−2,… is 6.

Answer: 6.