Arithmetic Progression

[madhur_ahuja]

In a certain quiz that consists of 10 questions, each
question after the first is worth 4 points more than
the preceding question. If the 10 questions on the
quiz are worth a total of 360 points, how many point
is the third question worth?

A.18
B.24
C.26
D.32
E. 44

[ssmiles08]

IMO C.

I usually first look at the patterns the arithmetic progression is making.

here it is:
x
x+4
x+4+4
x+4+4+4...

you are finding the sum of all 10 numbers. Notice that this pattern of numbers creates an evenly spaced set containing each number that is 4 away from the next one.

Also notice that the 10th number will have 4*9 added to x

avg: [x+(x+4*9)]/2

sum = avg* (#of terms)

2x + 36 = (360*2)/10

x = 18

so the third number is x + (4*2) = 18 + (8) = 26.

(C)


OA?

[truplayer256]

The first question is worth x points, the second question is worth x+4 points, the third question is worth x+8 points and so on.

As you indicated in your post, we have an arithmetic progression and the total number of points on the quiz add up to 360. So if we add everything up: x+x+4+x+8.....x+4n, we get 10x plus something equals 360. Now what is that something? Let's use our formula for the sum of an arithmetic progression: Sn=n/2(a1+an) where n represents the total amount of numbers in the progression, a1 represents the first number in the progression, and an represents the last number in the progression. There are a total of 9 numbers in the progression, with the first digit being 4 and the last digit being 36, so:

Sn=9/2(40)=180

Now that we've found that something, let's solve for x.

10x+180=360

x=18

1st question is worth 18 points and the third question is worth 18+8 or 26 points. C