Suming values that increase by constant over extended period

Question

 if on the first day I get $10 and on the second day I get 2*$10 ($20) and the 3rd day I get 3*$10 ($30), how much money will I have after 30 day.

Answer 1

That is an arithmetic sequence. The problem is asking what is the sum of the first 30 terms of the arithmetic sequence. The problem gives you the first 3 terms of the sequence (the first 3 days).

 

You have two ways to solve this problem:

 

1) You write down all 30 terms of the sequence (all 30 days) and add them.

 

or

 

2) Use the formula of the arithmetic series: S_n = n(a₁+a_n)/2 where a₁ is the first term of the sequence (day 1) and a_n is the last term of the sequence (day 30) and n=30