Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.2 Arithmetic Sequences and Series - 14.2 Exercise Set - Page 903: 48

$S_{20}=\$42500.$

If Carrie saves money in an arithmetic sequence: $\$$700 for the first year, $ \$ $850 the second etc. then $a_1=\$700$ and $d=a_2-a_1=\$850-\$700=\$150$. For the twentieth year she saves $a_{20}=a_1+d(20-1)$ $a_{20}=\$700+\$150\cdot19=\$3550.$ In general, in twenty years she will have money $S_n=\dfrac{a_1+a_n}{2}n=\dfrac{\$700+\$3550}{2}20=\$42500$