Don saves $1 the first week, 2$ the second week, $3 the third week, and $4 the fourth week. if he continues in this way, how many weeks will it take before don has saved at least $50?
show me the simplest and quickest way to solve this problem. explain your steps

This forms an arithmetic sequence, where the first term = 1, common difference = 1, and number of terms = n.

The formula for the sum of an arithmetic sequence is 



Where a = the first term and d = the common difference.

We want the sum to be at least $50, so


Substituting in a and d


Rearranging












So it will take 9.51 weeks, or 10 weeks to the nearest week.