4, 7, 12, 21, 36, ?

Solution

ATQ, From 4 to 7, the difference is 7−4=37−4=3. From 7 to 12, the difference is 12−7=512−7=5. From 12 to 21, the difference is 21−12=921−12=9. From 21 to 36, the difference is 36−21=1536−21=15. Looking at the differences 3,5,9,153,5,9,15, we see that the gaps between these differences are increasing by an even number each time: 22 (from 3 to 5), 44 (from 5 to 9),66 (from 9 to 15). So, the next difference should increase by 88, which means the next difference should be 15+8=23 Thus, the next term in the series should be 36+23=59 Therefore, the number that comes in place of "?" in the series 4, 7, 12,21,36,? is 59