Given the arithmetic sequence 11, 5, -1, ..., find . [Show
all work.] how to solve?
find what?
the common difference is -6
yes a = 11 , d = -6
https://www.mathsisfun.com/algebra/sequences-series.html
To find the sum of an arithmetic sequence, you need to know the first term (a1), the common difference (d), and the number of terms (n).
In this case, the first term (a1) is 11, and the common difference (d) can be found by subtracting any two consecutive terms.
The second term (a2) is 5, so we can find the common difference by subtracting 5 from 11: d = 5 - 11 = -6.
To find the number of terms (n), we need to identify the pattern in the sequence. Here, we subtract 6 from each term to get the next term. So, to find the n-th term, we subtract 6 n times from the first term.
Let's find the n-th term in the sequence using the formula: an = a1 + (n-1)d.
In this case, we have the first term a1 = 11 and the common difference d = -6. Let's find the n-th term by substituting these values into the formula:
a_n = 11 + (n-1)(-6)
a_n = 11 - 6n + 6
a_n = 17 - 6n
Since we don't know the value of n, we cannot determine the exact term in the sequence. However, we can see that each term will increase by 6. So, the sequence can continue indefinitely.
To find the sum of the sequence, we will use the formula for the sum of an arithmetic series:
Sn = (n/2)(a1 + a_n)
Now we have the necessary information to find the sum. However, since the number of terms is not provided, we cannot determine the sum without this information.