That's fine. It's certainly faster than the algebra version.
5 + k*4 > 200
k*4 > 195
k > 48.5 ==> k = 49
5 + 49*4 = 5 + 196 = 201
Your modular arithmetic is to be commended.
Now add them up.
Q) The first two terms in an arithmetic progression are 5 and 9. The last term in the progression is the only term which is greater than 200. Find the sum of all the terms in the progression.
What I did was figure out the difference of each term, which came out to be 4 for me, and it is the correct value.
Next I attempted to get the number of terms in this AP, for that I needed the last term of this AP. So I looked at the first two terms and each are 1 more than the multiple of 4. So as 200 is divisible by 4, I choose 201 as the final term (choose 1 more than the multiple of 4 considering the first two terms)
Is this correct?