Kenneth O. answered • 03/26/21
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The long way would be to add $100, $101, ... $119.
The formula for these problems is 100n + (n-1)(xn/2)
where n is the number of payments and x is increment by which payment increases.
So, $100 * 20 + (20 - 1)(($1*20)/2)
or 2000 + 19(10)
or 2190.
Kenneth O.
tutor
The $100 * 20 does not account for the $1 more per week. The second part of the equation deals with that by taking the average of the $1 and the $19, the $2 and the $18, the $3 and the $17, etc. That is where the (1*20)/2 comes into play.
To understand this better, look at the same rules, but only for 4 weeks.
100+101+102+103 is easy enough to calculate.
But what do we have? 100 + 100 + 1 + 100 + 2 + 100 + 3
So we have $100 * 4 (weeks) + (1+2+3)
1+2+3 is the same as 2 + 2 + 2 or 3 *2.
(4 weeks - 1) = 3 weeks paying an average of $2
4 weeks * 100 + 3 weeks * $2 = $406
Does that help?
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03/26/21
Sally F.
But don't you have to deposit $1 more than you deposited the week before? Wouldn't you add the previous week each time plus 1?03/26/21