Find the sum of the first 5 terms of the arithmetic sequence whose general term is a(n) = 7(n) - 1.
S5 = 5/2 (a_1 + a_5)
Now just plug in your values for the two terms.
To find the sum of the first 5 terms of the arithmetic sequence, you need to apply the formula for the sum of an arithmetic series.
The general term of the arithmetic sequence is given by a(n) = 7n - 1.
First, let's find the first term of the sequence (a1) by substituting n = 1 into the formula:
a(1) = 7(1) - 1
a(1) = 6
Next, let's find the common difference (d) by subtracting the second term (a2) from the first term (a1):
d = a(2) - a(1)
d = (7(2) - 1) - (7(1) - 1)
d = 13 - 6
d = 7
Now that we know the first term (a1 = 6) and the common difference (d = 7), we can use the formula for the sum of an arithmetic series:
Sn = (n/2)(a1 + an),
where Sn represents the sum of the first n terms of the sequence.
Substituting the values, we have:
S5 = (5/2)(a1 + a5)
To find a5, substitute n = 5 into the general term formula:
a(5) = 7(5) - 1
a(5) = 35 - 1
a(5) = 34
Now we can calculate the sum:
S5 = (5/2)(a1 + a5)
S5 = (5/2)(6 + 34)
S5 = (5/2)(40)
S5 = 5 * 20
S5 = 100
Therefore, the sum of the first 5 terms of the arithmetic sequence is 100.