Explanation:
I think the first one is the answer
Answer:
Emma is kind and knows justice. she also has compassion for others.
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
![\frac{a_{1}+a_{n}}{2}n = \frac{10 + 10+5(n-1)}{2} n =175](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba_%7B1%7D%2Ba_%7Bn%7D%7D%7B2%7Dn%20%3D%20%5Cfrac%7B10%20%2B%2010%2B5%28n-1%29%7D%7B2%7D%20n%20%3D175%20%20%20)
![n^{2}+3n-70=0](https://tex.z-dn.net/?f=%20n%5E%7B2%7D%2B3n-70%3D0%20%20)
![n_{1} = -10 , n_{2}=7](https://tex.z-dn.net/?f=%20n_%7B1%7D%20%3D%20-10%20%2C%20n_%7B2%7D%3D7%20%20%20)
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.