Nick opens a savings account with $50. Each week after, he deposits $15. In how many weeks will he have saved $500?

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Answer 1 · 2017-04-13T17:06:25

After $30$ weeks he has $$500$

We are working with an arithmetic series, where each term representswthe total in the account after $15$ is added each week.

The sequence is $" "50," "65," "80," "95 ....... 500$

We are looking for $(n-1)$ weeks

After 1 week, we have the 2nd term,
After 2 weeks we have the 3rd term ....

We know that $T_n = $500," " a = 50," " d = 15$

$Tn = a +(n-1)d$

$50+(n-1)15 = 500$

$(n-1)15 = 500-50 =450$

$n-1 = 450/15 = 30$

Therefore after 30 weeks he has $$500$