As you can see, the difference between two consecutive months is :
707.60-740=-32.4
and it is the same for third-second and fourth-third.
So we have indeed an arithmetic sequence where d=-32.4
Now, we have a1=740
so the general term of the sequence:
an = a1 + (n-1)d
an = 740 + (n-1)*(-32.4)
an=772.4 -32.4n
an tells us how much money there is in the account in the nth month.
now we need to check when an=0 (the money is over)
772.4 = 32.4n
n = 23.8
but this is not an integer and we are counting months
so we will take 23 cause clearly for 24 we will have minus!
so n = 23. -> the account is good without depositing for 23 months (including the first)
