Question

Veronica is saving money to by a saddle for her horse that costs 175 . She plans to save $10 the first month and then increased amount she say's by five each month after the first month how many months will take her to say 175

Answer 1

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

$\frac{a_{1}+a_{n}}{2}n = \frac{10 + 10+5(n-1)}{2} n =175$

$n^{2}+3n-70=0$

$n_{1} = -10 , n_{2}=7$

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.

Answer 2

It will take her 7 months. 10+15+20+25+30+35+40=175 remember she is increasing the amount by 5 each month