Given series: $2,\,7,\,14,\,23,\,34,\,\_\_$

Find the differences:

$7-2=5$,   $14-7=7$,   $23-14=9$,   $34-23=11$

Difference pattern: $5,\,7,\,9,\,11$ (increases by 2 each time)

Next difference $= 11 + 2 = 13$

Next term $= 34 + 13 = 47$

Answer: $\boxed{47}$ ✅

Given series: $6,\,20,\,42,\,72,\,110,\,\_\_$

First differences: $14,\,22,\,30,\,38$

Second differences: $8,\,8,\,8$ (constant)

Next first difference $= 38 + 8 = 46$

Next term $= 110 + 46 = 156$

Answer: $\boxed{156}$ ✅