Mathematics I / Arithmetic and Geometric Sequences
Practice question · Put in order

Order the steps of finding the sum 3 + 6 + 12 + ... + 384.

Hints
  1. You cannot use the sum formula until you know how many terms there are.
  2. 384 divided by 3 is 128, which is 2 to the seventh.
Show the answer
  1. Identify the first term as 3 and the common ratio as 2
  2. Solve 3 x 2 to the power n - 1 = 384 to find that there are 8 terms
  3. Apply the finite geometric sum formula S_n = a_1 (r to the n, minus 1) divided by (r - 1)
  4. Compute 3 x (256 - 1) divided by 1, giving 765
Why

Identify a_1 and r, count the terms, then apply the formula. Here 384 = 3 x 2 to the seventh, so n = 8, and S_8 = 3(2 to the eighth minus 1)/(2 - 1) = 3(255) = 765. Adding the eight terms by hand confirms it.

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