If a person puts 1 cent in a piggy bank on the first day, 2 cents on the second day, 3 cents on the third day, and so forth, how much money will be in the bank after 40 days? $8.20 $16.40 $0.40 $4.10

This is an arithmetic sequence with the common difference being 1

and if u have 1 cent on day 1 and 2 cents on day 2 ... then on day 40, u would have 40 cents ... but we need the sum of all the days ...

the sum of an arithmetic sequence can be found using the formula:

sn = n (a1 + an) / 2

n = number of terms = 40

a1 = first term = 1

an = last term = 40

now we sub

s (40) = 40 (1 + 40) / 2

s (40) = 40 (41) / 2

s (40) = 1640/2

s (40) = 820 ... 820 cents = $ 8.20 < = = the sum