This is quick working out
Q1)
n=1, 5+2(11) = 27 which is divisible by 3
Assumption: n=k, 5^k + 2 x 11^k = 3M (where M is an integer)
Proof: n=k+1,
5^(k+1) + 2 x 11^(k+1)
= (5 x 5^k) + (2 x 11 x 11^k)
Now look at the assumption and times it by 5 -----> 5 x 5^k + 10 x 11^k = 15M...