106 is the nth term for the sequence 1, 8, 15, 22...?

nth = F + (N -1)D

106 =1 + (N-1)*7

106 =1 + 7N - 7

106 - 1 + 7 = 7N

112 = 7N divide both sides by 7

N = 112 / 7

N = 16th term in your sequence.

The common difference between terms is 7

So....we can solve this

106 =  1  + 7(n - 1)   simplify

106  = 1 + 7n - 7

106  = 7n  - 6     add 6 to both sides

112  = 7n           divide both sides by 7

16  = n    →    i.e,  the 16th term