What is the common difference of a 43–term arithmetic sequence where the first term is –13 and the sum is 9,374?

Umm, I don't get it the 4 terms of 43 and 3 are not that pls help!!! what the heck pls help so the first term is 43 and the common difference is 3 what is the answer to my question what is the answer? I don't get it I'm so confused! help pls I don't get it what do u mean help! help pls what is the answer

Umm, I don't get it the 4 terms of 43 and 3 are not that pls help!!! what the heck pls help so the first term is 43 and the common difference is 3 what is the answer to my question what is the answer? I don't get it I'm so confused! help pls I don't get it what do u mean help! help pls what is the answer pls answer I do not get it very confused

To find the common difference of an arithmetic sequence, we need to know the first term, the number of terms, and the sum of the sequence.

In this case, we know that the first term (a₁) is -13 and the sum (S) is 9,374. However, we don't have the number of terms (n) directly.

To find the number of terms, we can use the formula for the sum of an arithmetic sequence:

S = (n/2) * (2a₁ + (n-1)d)

where S is the sum, n is the number of terms, a₁ is the first term, and d is the common difference.

Let's plug in the given values:

9,374 = (n/2) * (2 * -13 + (n-1)d)

Now, we need to solve this equation to find the value of n.

Next, we can rearrange the equation to isolate d:

9,374 = (n/2) * (-26 + (n-1)d)
18,748 = n*(-26) + (n-1)*(n-1)d
18,748 = -26n + (n^2 - 2n + 1)d
18,748 = (n^2 - 28n + 1)d - 26n

Now, since we know that the number of terms is a positive whole number, we can solve this equation by considering the factors of 18,748. We can look for two factors such that their difference is equal to -2.

By factoring 18,748, we find that 18748 = 2^2 * 37 * 127. Among these factors, we can see that 37 and 127 have a difference of 90 (127 - 37 = 90). However, this difference is not equal to -2.

Therefore, this means that there is no positive whole number value of n that will satisfy the equation, and therefore, the given arithmetic sequence cannot have a sum of 9,374.

In this case, there seems to be an error or missing information in the question.