The given arithmetic sequence starts at 3 and increases by 6 for each subsequent term. To find the sum of the first 34 terms of this sequence, we can use the formula for the sum of an arithmetic series.
The sum S of the first n terms of an arithmetic sequence can be calculated using the formula:
S = n/2 * (a + l)
Where:
- S = Sum of the first n terms
- n = Number of terms
- a = First term
- l = Last term
For our sequence:
- a = 3
- n = 34
Next, we need to find the last term in the sequence, l. The last term can be found using the formula for the nth term of an arithmetic sequence:
l = a + (n-1) * d
Where:
- d = common difference (which is 6 in this case)
So:
l = 3 + (34-1) * 6 = 3 + 198 = 201
Now we have all the components we need to calculate the sum:
S = 34/2 * (3 + 201)
S = 17 * 204 = 3468
Therefore, the sum of the arithmetic sequence consisting of the first 34 terms is 3468.