To find the sum of a finite geometric sequence, we first need to identify the first term and the common ratio. In this case, we have the expression 34n, which gives us the terms for n = 1 to n = 5:
- For n = 1: 34 × 1 = 34
- For n = 2: 34 × 2 = 68
- For n = 3: 34 × 3 = 102
- For n = 4: 34 × 4 = 136
- For n = 5: 34 × 5 = 170
The sequence obtained is 34, 68, 102, 136, and 170. Now, we can see that this represents a finite arithmetic series rather than a geometric sequence, as each term increases by a common difference rather than multiplying by a common ratio.
To find the sum of these terms, we can simply add them together:
- Sum = 34 + 68 + 102 + 136 + 170
Calculating this gives:
- Sum = 34 + 68 = 102
- Sum = 102 + 102 = 204
- Sum = 204 + 136 = 340
- Sum = 340 + 170 = 510
Therefore, the total sum of the sequence from n = 1 to n = 5 is 510.