The first one looks like it's trying to be the Fibonacci sequence  should 12 be 13?
In any case although there is a formula for the nth term that would be of no use here : you need to spot the pattern (add the last two numbers together) and it will grow quite quickly to be a 3 digit number 2,3,5,8,13,21,34,55,89  the next one is obviously 3 digit without even needing to work it out
The second one: again there is probably a general formula, but expecting a child to remember every possible formula for every possible version of the question is less useful than equipping them with the reasoning skills to work it out from scratch
So one way to do it would be think first:
how many different places can there be NOT a 7 if there are two 7s?
Answer  3
How many different not7 digits can go in that place?
Answer  9 (0,1,2,3,4,5,6,8,9)
Have we missed any  Yes  the number 777
Have we overcounted? Yes  we can't count 077 as it's not a 3 digit number
So the final answer is...... ????
Systematic thinking and patternspotting are the skills being looked for
