Marco took a bunch of candies and divided them into 3 even groups. If each group has 21 candies, how many candies are there?
2 answers:
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We know f(x)=5x+1. Plug in f(x) in the g(x) function.
We get
Distribute the 2 to 5x and 1.
Simplify to get
Now, we plug in -1 for x.
We get
Simplify to get
Now, we plug in -1 for x.
Here's a pattern to consider:
1+100=101
2+99=101
3+98=101
4+97=101
5+96=101
.....
This question relates to the discovery of Gauss, a mathematician. He found out that if you split 100 from 1-50 and 51-100, you could add them from each end to get a sum of 101. As there are 50 sets of addition, then the total is 50×101=5050
So, the sum of the first 100 positive integers is 5050.
Quick note
We can use a formula to find out the sum of an arithmetic series:
Where s is the sum of the series and n is the number of terms in the series. It works for the above problem.
1+100=101
2+99=101
3+98=101
4+97=101
5+96=101
.....
This question relates to the discovery of Gauss, a mathematician. He found out that if you split 100 from 1-50 and 51-100, you could add them from each end to get a sum of 101. As there are 50 sets of addition, then the total is 50×101=5050
So, the sum of the first 100 positive integers is 5050.
Quick note
We can use a formula to find out the sum of an arithmetic series:
Where s is the sum of the series and n is the number of terms in the series. It works for the above problem.