Let S1= 1, S2=2+3, S3= 4+5+6
Find S7
Find S17
Find Sn

Each term Sₙ consists of the sum of a triangular number of terms, which are given by

The triangular numbers are given recursively for n ≥ 1 by

starting with T₀ = 0.

For example,

• S₁ = 1 and

• S₂ = 2 + 3 and

• S₃ = 4 + 5 + 6 and

Then the n-th term of the sequence we're considering is

Expanding this sum, we have

There are n terms on the right side, and hence n copies of , and the rest of the terms make up the next triangular number :

We have a closed form for , so we end up with

From here it's easy to find S₇ and S₁₇.

11

step-by-step explanation:

32.50-7.50=25

225/25=11