To calculate the sum of the finite arithmetic sequence defined by the expression 4n + 10 for values of n ranging from 1 to 18, we first need to derive the terms of this sequence for each integer value of n within that range.
1. **Calculate the terms:** We substitute values of n from 1 to 18 into the expression:
- For n = 1: 4(1) + 10 = 14
- For n = 2: 4(2) + 10 = 18
- For n = 3: 4(3) + 10 = 22
- For n = 4: 4(4) + 10 = 26
- For n = 5: 4(5) + 10 = 30
- For n = 6: 4(6) + 10 = 34
- For n = 7: 4(7) + 10 = 38
- For n = 8: 4(8) + 10 = 42
- For n = 9: 4(9) + 10 = 46
- For n = 10: 4(10) + 10 = 50
- For n = 11: 4(11) + 10 = 54
- For n = 12: 4(12) + 10 = 58
- For n = 13: 4(13) + 10 = 62
- For n = 14: 4(14) + 10 = 66
- For n = 15: 4(15) + 10 = 70
- For n = 16: 4(16) + 10 = 74
- For n = 17: 4(17) + 10 = 78
- For n = 18: 4(18) + 10 = 82
2. **List of the terms:** The generated terms from n = 1 to n = 18 are:
[14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82]
3. **Sum of the terms:** To find the sum of this sequence, we can use the formula for the sum of an arithmetic sequence:
The formula for the sum S of the first n terms of an arithmetic sequence is given by:
S = (n/2) * (first term + last term)
In our case:
- n = 18 (the number of terms)
- first term = 14
- last term = 82
4. **Applying the formula:** Substituting these values into the formula, we get:
S = (18/2) * (14 + 82)
S = 9 * 96
S = 864
5. **Final Result:** Therefore, the sum of the arithmetic sequence from n = 1 to n = 18 for the expression 4n + 10 is 864.