Longer way:
1st year: $100
2nd year: $150
3rd year: $200
4th year: $250
5th: $300
6th: $350
7th: $400
8th: $450
9th: $500
10th: $550
Total = $100 + $150 + $200 + $250 + $300 + $350 + $400 + $450 + $500 + $550
= $3250
Shorter way:
Total = [tex] \frac{n}{2} (2a+(n-1)d)[/tex],
where a is first term, n is number of terms, d is common difference (what is added/subtracted to get the next term in the sequence)
Total = [tex] \frac{10}{2} (2*100+(10-1)50) \\
= 5(200 + 9*50) \\
= 5(200+450)
= 3250[/tex]
