This is an issue that I see again and again in your questions, so I will explain it in a different way.

Let’s say that we have a list of values, like 47, 2, 87, 40, 84, 35, 65, 34, 55, 99. We want to calculate their total, that is, the sum of all the values.

We can write

`<- 47 + 2 + 87 + 40 + 84 + 35 + 65 + 34 + 55 + 99 total `

but this gets complicated when we have more numbers. We can do the sum step-by-step

```
<- 0
total <- total + 47
total <- total + 2
total <- total + 87
total <- total + 40
total <- total + 84
total <- total + 35
total <- total + 65
total <- total + 34
total <- total + 55
total <- total + 99 total
```

We can see that the final result will be the same. The difference is
that we start with an initial value for `total`

, and we
update it several times, taking the old value, adding the new number,
and storing the updated value in the same place.

We are recycling the variable. By the way, these are called
*variables* because they can *vary*, or change.

Imagine now that instead of fixed numbers, you have a list. Let’s say
that the list is called `values`

, and there are 10 numbers on
it. Now we can write

```
<- 0
total <- total + values[[1]]
total <- total + values[[2]]
total <- total + values[[3]]
total <- total + values[[4]]
total <- total + values[[5]]
total <- total + values[[6]]
total <- total + values[[7]]
total <- total + values[[8]]
total <- total + values[[9]]
total <- total + values[[10]] total
```

As before, we get the sum of all values at the end. Wise people will find a way to tell the computer to do all the work.

Two final comments:

- We used
`values[[1]]`

because we assumed that`values`

is a list - The elements of
`values`

can be vectors. They must have all the same size, and we would need to start with`total <- rep(0, N)`

- You have to find what is
`N`

in this case.

- You have to find what is