The sequence defined by the formula 4n + 3 can be analyzed for its first ten terms. To calculate the sum, we first need to determine each of the first ten terms:
- For n = 1:
4(1) + 3 = 4 + 3 = 7 - For n = 2:
4(2) + 3 = 8 + 3 = 11 - For n = 3:
4(3) + 3 = 12 + 3 = 15 - For n = 4:
4(4) + 3 = 16 + 3 = 19 - For n = 5:
4(5) + 3 = 20 + 3 = 23 - For n = 6:
4(6) + 3 = 24 + 3 = 27 - For n = 7:
4(7) + 3 = 28 + 3 = 31 - For n = 8:
4(8) + 3 = 32 + 3 = 35 - For n = 9:
4(9) + 3 = 36 + 3 = 39 - For n = 10:
4(10) + 3 = 40 + 3 = 43
The first ten terms are: 7, 11, 15, 19, 23, 27, 31, 35, 39, 43
Now, let’s calculate the sum of these terms:
- 7 + 11 = 18
- 18 + 15 = 33
- 33 + 19 = 52
- 52 + 23 = 75
- 75 + 27 = 102
- 102 + 31 = 133
- 133 + 35 = 168
- 168 + 39 = 207
- 207 + 43 = 250
Thus, the sum of the first 10 terms of the sequence 4n + 3 is 250.