Question

Chu-Li has $100 in her piggy bank. How much will she have in her bank 40 weeks from now if she puts $1 in the bank next week, $2 two weeks from now, $3 three weeks from now, and continues to increase the amount that she puts in by $1 each week?

Answer 1

$920

Explanation:

The amounts added are the arithmetic sequence ...

1, 2, 3, ... 40

The average term of this sequence is (1 +40)/2 = 20.5. The sum of the terms of this sequence is the number of terms (40) multiplied by the average term (20.5). That product is ...

40·20.5 = 820

Chu-Li will have added $820 to her bank in 40 weeks, so the total there is ...

$100 +820 = $920 . . . amount Chu-Li will have 40 weeks from now