To evaluate the summation of the expression -5n – 1 from n = 3 to n = 12, we will follow these steps:
- Identify the expression: The expression we are summing is -5n – 1.
- Set the limits: We need to calculate the sum for values of n starting from 3 up to 12.
- Calculate the summation: We will compute the value for each integer n within these bounds and then add them together:
Calculating each term:
| n | Value of -5n – 1 |
|---|---|
| 3 | -5(3) – 1 = -15 – 1 = -16 |
| 4 | -5(4) – 1 = -20 – 1 = -21 |
| 5 | -5(5) – 1 = -25 – 1 = -26 |
| 6 | -5(6) – 1 = -30 – 1 = -31 |
| 7 | -5(7) – 1 = -35 – 1 = -36 |
| 8 | -5(8) – 1 = -40 – 1 = -41 |
| 9 | -5(9) – 1 = -45 – 1 = -46 |
| 10 | -5(10) – 1 = -50 – 1 = -51 |
| 11 | -5(11) – 1 = -55 – 1 = -56 |
| 12 | -5(12) – 1 = -60 – 1 = -61 |
Summing the values:
Now, we will add all the computed values:
S = -16 + (-21) + (-26) + (-31) + (-36) + (-41) + (-46) + (-51) + (-56) + (-61)
S = -16 – 21 – 26 – 31 – 36 – 41 – 46 – 51 – 56 – 61
S = – 6
+ – 8 = -6 + -8 = -73
Thus, the final result for the summation of -5n – 1 from n = 3 to n = 12 is -505.