How do I use subtraction and addition intermittently on a vector?

How to Use Subtraction and Addition Intermittently on a Vector?

To use subtraction and addition intermittently on a vector, you can use the following methods:

Method 1: Using a Custom Formula

2 * x[1] + sum(x*(-1)^seq_along(x))

This formula multiplies the first element of the vector (x[1]) by 2, then adds the remaining elements multiplied by (-1) to the power of their position in the vector. For example, if x = [1, 2, 3, 4, 5], this formula will calculate (2 * 1) + (2 * (-1)) + (3 * (-1)^2) + (4 * (-1)^3) + (5 * (-1)^4), which equals -1.

Method 2: Using Vector Indexing 1) First, note that the first two elements are both positive, but after that, they are alternating, so treat 1 separately, extract the even and odd position elements after the first, and sum each, and then subtract the two sums, adding x[1]. Note that this requires that x have a length of 3 or more.

x <- 1:5

x[1] + sum(x[-1][c(TRUE, FALSE)]) - sum(x[-1][c(FALSE, TRUE)])
## [1] -1

# check
1+2-3+4-5
## [1] -1

2) This can also be written as:

sum(x[1], x[-1][c(TRUE, FALSE)], - x[-1][c(FALSE, TRUE)])
## [1] -1

3) This solution works even if the length of x is 0, 1, or 2 as well. We create the vector c(1, 1, -1, 1, -1, ...) and multiply it by x and sum.

sum(replace(rep(c(-1, 1), length = length(x)), 1, 1) * x)
## [1] -1

Method 3: Using the c() Function

Here is a way. It will recycle the vector c(1, -1) to the length of x. If the length of x is not even, it gives a warning that must be suppressed since that is expected.

x <- 1:5
sum(c(1, -1) * x) |> suppressWarnings()
#> [1] 3

Edit:

ThomasIsCoding found a bug in the above code. Here is his correction.

x <- 1:5
(x[1] + sum(c(1,-1)*x[-1])) |> suppressWarnings()
#> [1] -1