How do you evaluate the summation of -2n – 3 from n equals 2 to 10?

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To evaluate the summation of the expression -2n – 3 from n = 2 to n = 10, we start by rewriting the summation in mathematical notation:

∑n=210 (-2n – 3)

Now, let’s break this down step-by-step:

  1. Calculate Individual Terms: We evaluate the expression for each integer value of n from 2 to 10:
    • 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
  2. Sum the Individual Terms: Now that we have the values for each n, we can add them together:
    • -7 + -9 + -11 + -13 + -15 + -17 + -19 + -21 + -23
  3. Calculate the Total: Adding these together gives:
    • -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 summation of -2n – 3 from n = 2 to n = 10 results in:

-135

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