How do you find the sum number of an arithmetic sequence? I forgot and my textbook does not explain it well.
depends what information you know
1. If you know the first term a, and the common difference d, and the number of terms n, then
Sum(n) = n/2[2a + (n-1)d]
2. If you know the first term a and the last term l, and the number of terms n, then
Sum(n) = n/2(a+l)
N = the term number right?
I'm not sure what you mean by "term number."
"n" typically refers to how many units you have, how many numbers you are dealing with, the number of scores.
"a" is the value of the first number. Is that what you mean by "term number"?
I hope this helps a little more. Thanks for asking.
To find the sum of an arithmetic sequence, you can use the following formula:
S = (n/2)(2a + (n-1)d)
Where:
S = the sum of the sequence
n = the number of terms in the sequence
a = the first term of the sequence
d = the common difference between successive terms
To apply this formula, follow these steps:
1. Identify the values of a, d, and n in the given arithmetic sequence.
- The first term, a, is the value of the sequence's initial term.
- The common difference, d, is the constant difference between any two successive terms in the sequence.
- The number of terms, n, is the total count of terms in the sequence.
2. Substitute the identified values into the formula:
S = (n/2)(2a + (n-1)d)
3. Perform the necessary calculations according to the order of operations (PEMDAS/BODMAS) to find the sum, S.
For example, let's say we have an arithmetic sequence with a first term, a, equal to 3, a common difference, d, equal to 2, and the number of terms, n, equal to 10. We can calculate the sum of this sequence as follows:
S = (10/2)(2(3) + (10-1)(2))
= (5)(6 + 9(2))
= (5)(6 + 18)
= (5)(24)
= 120
Therefore, the sum of the arithmetic sequence with the given parameters is 120.