To find the sum of the arithmetic sequence given by the expression 2n + 5 from n = 1 to n = 15, we first need to calculate each term of the sequence for the specified values of n.
We can calculate the terms of the sequence:
- When n = 1: 2(1) + 5 = 7
- When n = 2: 2(2) + 5 = 9
- When n = 3: 2(3) + 5 = 11
- When n = 4: 2(4) + 5 = 13
- When n = 5: 2(5) + 5 = 15
- When n = 6: 2(6) + 5 = 17
- When n = 7: 2(7) + 5 = 19
- When n = 8: 2(8) + 5 = 21
- When n = 9: 2(9) + 5 = 23
- When n = 10: 2(10) + 5 = 25
- When n = 11: 2(11) + 5 = 27
- When n = 12: 2(12) + 5 = 29
- When n = 13: 2(13) + 5 = 31
- When n = 14: 2(14) + 5 = 33
- When n = 15: 2(15) + 5 = 35
Now, we list all the terms: 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35.
Next, we find the sum of these terms. The sum of an arithmetic sequence can also be calculated using the formula:
Sum = (Number of terms) × (First term + Last term) / 2
Here, the number of terms is 15, the first term is 7, and the last term is 35.
So, we calculate:
Sum = 15 × (7 + 35) / 2
This simplifies to:
Sum = 15 × (42) / 2 = 15 × 21 = 315
Therefore, the sum of the finite arithmetic sequence from n=1 to n=15 using the expression 2n + 5 is 315.