Chapter 2 - Reasoning and Proof - 2-1 Patterns and Inductive Reasoning - Practice and Problem-Solving Exercises - Page 85: 25

10,000

Find the first few sums and look for a pattern 1 term, 1=1 2 terms 4=$2^2$ 3 terms 9=$3^2$ 4 terms 16=$4^2$ The sum is the number of the term squared. The value of the $n^{th}$ term is $n^2$, so the 100th term will be $100^2=10000$.