<p>on his first day as a telemarketer, Marshall made 24 calls. His goal was to make 5 more calls on each successive day than he had made the day before. If Marshall met, but did not exceed, his goal, how many calls had he made in all after spending exactly 20 days making calls as a telemarketer?Update : PLEASE SHOW EQUATIONUpdate 2: THE CHOICES ARE
A) 670
B) 690
C) 974
D) 1430
E) 1530</p>
<p>I know you can plug in numbers and add all the figures to get the solution, but is there a quicker way to solve this problem? Please help me out, I am so very desperate....</p>
<p>Put x as the days of being a telemarketer.
y is equal to the calls that he made. </p>
<p>y=(5x-5)+24</p>
<p>The first day, he made 24 calls, the next day, he made 29 and so on. This equation works. </p>
<p>In order to add it up, you use a geometric sequence. Look it up if you don’t know what it is. </p>
<p>Edit: Haha this might be the geometric sequence that Hawkace was talking about. </p>
<p>Another approach which uses @Hawkace 's equation is this: (I forget what kind of method this is, it’s named after a guy and it always works finding sums with a question like this)</p>
<p>Notice how Day 1 and Day 20 add up to 143 :
First day: (5<em>1-5) +24 = 24
Last day: (5</em>20-5) +24 = 119
24+119 = 143</p>
<p>Notice how Day 2 and Day 19 also add up to 143:
Day 2 = 29
Day 19= 114 </p>
<p>This pattern repeats itself when you pair up Day 3 and Day 17, Day 4 and Day 16, and so on. </p>
<p>There are 10 paired up days so 143 *10 = 1430</p>
<p>Another method that my ACT proposes has an equation that you’re looking for, is a bit more confusing in my opinion but helpful if you remember. I don’t really know this well, I’m just writing down what the book saysSum of an arithmetic series:</p>
<p>Sum = n/2[2a + (n-1)d]</p>
<p>a is the first term (or day in this case) in the series: 24
d is the common difference between each terms: 5
n is the number of terms in the series: 20</p>
<p>So plugged in, it would look like this: 20/2[2*24 +(20-1) *5] =</p>
<p>10[48+(19*5)] =
10 *143</p>
<p>Hope this helps. </p>
<p>@K1Helen Riemann sums. =D> </p>