Question

pattern rule for 1,2,5,14,41

Answer 1

The difference between 2 terms is expressed in the form of
${3}^{n}$
Where n starts from 0,1,2,3
$2 - 1 = 1 = {3}^{0} \\ 5 - 2 = 3 = {3}^{1} \\ 14 - 5 = 9 = {3}^{2} \\ 41 - 14 = 27 = {3}^{3}$
The next no. will be
$41 + {3}^{4} \\ = 41 + 81 \\ = 122$