#### Explanation:

Her salary which increases every year forms a geometric sequence.

35,000 ; 38,500 ; 42,350 .......

The common ratio is 1.1. (this can be found by dividing $\frac{{T}_{3}}{{T}_{2}}$)

or by realising that adding 10% onto 100% is the same as multiplying by $\frac{110}{100}$ which is the same as 1.1.

We are asked for her total earnings over 8 years. This now represents a geometric series:

35,000 + 38,500 + 42,350 + .......

There is a formula for the sum of the terms: ${S}_{n} = \frac{a \left({r}^{n} - 1\right)}{r - 1}$

${S}_{8} = \frac{35000 \left({1.1}^{8} - 1\right)}{1.1 - 1}$ = \$400,256.08