Chapter 12 Sequences and Series - 12.1 Define and Use Sequences and Series - Guided Practice for Examples 5 and 6 - Page 797: 14

285 apples

There are nine terms, ( $\displaystyle \sum_{n=1}^{9}$ ... ) and the nth term is $n^{2}$ (apples in nth layer) $\displaystyle \sum_{n=1}^{9}n^{2}=1^{2}+2^{2}+3^{2}+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}$ $=1+4+9+16+25 +36+49+64+81$ $=285$ Total: 285 apples in the stack.