Calculate the sum of each of the following arithmetic sequence:
1). 3+8+13+
The given arithmetic sequence has a common difference of 5.
To find the sum of an arithmetic sequence, we can use the formula:
Sn = n/2 * (a + l)
Where Sn is the sum of the sequence, n is the number of terms, a is the first term, and l is the last term.
In this case, the first term (a) is 3 and the common difference (d) is 5.
To find the last term (l), we can use the formula:
l = a + (n-1)*d
Here, a = 3 and d = 5. Let's assume n is the number of terms. Substituting these values into the formula, we get:
l = 3 + (n-1)*5
l = 3 + 5n - 5
l = 5n - 2
Since we know l is one of the terms in the given sequence, we can write it as:
5n - 2 = 13
Simplifying this equation gives us:
5n = 15
n = 3
Therefore, the last term (l) is 5n - 2 = 5(3) - 2 = 13.
Now that we have the values of n, a, and l, we can substitute them into the formula to find the sum (Sn):
Sn = n/2 * (a + l)
Sn = 3/2 * (3 + 13)
Sn = 3/2 * 16
Sn = 24
So, the sum of the arithmetic sequence 3, 8, 13 is 24.