We have to find when she will accumulate $175. If she saves $5 more for each month, then in the following months she will save 15, 20, 25 and so on. We can generalize this sequence as 10 + 5(n-1), where n is the number of the months. Applying the sum of nth formula of algebraic sequence, we can write
[tex] \frac{a_{1}+a_{n}}{2}n = \frac{10 + 10+5(n-1)}{2} n =175 [/tex]
[tex] n^{2}+3n-70=0 [/tex]
[tex] n_{1} = -10 , n_{2}=7 [/tex]
The correct answer is 7 months. We can check that for seven months she will save 15, 20, 25, 30, 35, 40 and including the first 10 dollar will sum up to 175 dollars.
