Carcass wrote:
In a sequence, each term is obtained by adding 4 to the preceding one. If the sum of the first 10 terms is equal to 80, what is the result of the addition of the first 40 terms?
A) 94
B) 320
C) 2,720
D) 27,200
E) 54,400
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITIONGRE - Math BookHere's another solution that requires only 1 formula:
Sum of the integers from 1 to n inclusive = (n)(n+1)/2 Let a = term1So, the sequence looks like this:
term1 = a
term2 = a
+ 4term3 = a
+ 4 + 4.
.
.
term10 = a +
+ 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4The sum of the first 10 terms is equal to 80So: 80 = (a) + (a
+ 4) + (a
+ 4 + 4) + .... + (a +
+ 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4)
80 = 10a +
a bunch of 4'sHow many
4's?
(1
four) + (2
fours) + (3
fours) + . . . + (9
fours)
Applying the formula, the sum of the integers from 1 to 9 = (9)(10)/2 = 45. So, there are 45
4's in the sum.
We get: 80 = 10a + (45)(
4)
Simplify: 80 = 10a + 180
We get: -100 = 10a
Solve: a = -10. Great, the first term is -10
What is the sum of the first 40 terms?Our sequence is as follows:
term1 = -10
term2 = -10
+ 4term3 = -10
+ 4 + 4term4 = -10
+ 4 + 4 + 4.
.
.
term40 = -10 + (
sum of 39 4's)
So, the sum of the first 40 terms = -400 +
a bunch of 4'sHow many
4's are there altogether?
(1
four) + (2
fours) + (3
fours) + . . . + (39
fours)
Applying the formula, the sum of the integers from 1 to 39 = (39)(40)/2 = 780
So, the sum of the first 40 terms = -400 + (780)(
4) = 2720
Answer: C