Rucha.Shukla
Howdy folks! Hope everyone’s prep is going fine

I wanted to know if there’s a more efficient way of solving below without listing all the terms (TIA!): Sn is a sequence such that it’s nth term is sum of first npositive integers. Tn is a sequence such that its first 2 terms are 1 and starting from the 3rd term, each term is the sum of the previous 2 terms. HOw many numbers less than 100 belong to both Sn and Tn ?
May not be the most elegant but a faster method could be knowing what Tn is looking for. It is talking of sum of first n positive integers, so nth term is n(n+1)/2, that is it is product of two consecutive numbers divided by 2. So, scan the Sn for these type of numbers. Sn = 1,1,2,3,5,8,13,21,34,55,89.........1*2/2 =1 , so 1...2*3/2=3, so 3....6*7/2=21, so 21.....7*8/2=28, not there...10*11/2=55, so 55