To evaluate the summation of the expression -2n – 3 from n = 2 to n = 10, we start by expressing the summation mathematically:
Σ (-2n – 3) from n = 2 to n = 10.
This means we need to calculate the value of the expression for each integer value of n from 2 to 10 and then sum these values:
- For n = 2: -2(2) – 3 = -4 – 3 = -7
- For n = 3: -2(3) – 3 = -6 – 3 = -9
- For n = 4: -2(4) – 3 = -8 – 3 = -11
- For n = 5: -2(5) – 3 = -10 – 3 = -13
- For n = 6: -2(6) – 3 = -12 – 3 = -15
- For n = 7: -2(7) – 3 = -14 – 3 = -17
- For n = 8: -2(8) – 3 = -16 – 3 = -19
- For n = 9: -2(9) – 3 = -18 – 3 = -21
- For n = 10: -2(10) – 3 = -20 – 3 = -23
Now, we can sum all these results:
-7 + (-9) + (-11) + (-13) + (-15) + (-17) + (-19) + (-21) + (-23) = -7 – 9 – 11 – 13 – 15 – 17 – 19 – 21 – 23
Calculating this step by step:
- -7 – 9 = -16
- -16 – 11 = -27
- -27 – 13 = -40
- -40 – 15 = -55
- -55 – 17 = -72
- -72 – 19 = -91
- -91 – 21 = -112
- -112 – 23 = -135
Thus, the final result of the summation is -135.