To find the sum of the first 30 terms of the arithmetic sequence 6, 13, 20, 27, 34, we first need to identify the first term and the common difference.
The first term (a) is 6, and we can find the common difference (d) by subtracting the first term from the second term:
d = 13 – 6 = 7.
The formula for the sum (S) of the first n terms of an arithmetic sequence is:
S_n = n/2 * (2a + (n – 1)d)
Where:
- S_n = the sum of the first n terms
- n = number of terms
- a = first term
- d = common difference
In this case, we have:
- a = 6
- d = 7
- n = 30
Now plugging those values into the formula:
S_30 = 30/2 * (2*6 + (30 – 1)*7)
S_30 = 15 * (12 + 29*7)
S_30 = 15 * (12 + 203)
S_30 = 15 * 215
S_30 = 3225
Therefore, the sum of the first 30 terms of this arithmetic sequence is 3225.