alleryStart learning →The terms of a series are given by 3k - 8 for k running from 1 to 12. What is the sum?
AS = 138
BS = 148
CS = 128
DS = 158
Answer & Solution
Correct answer: A. S = 138
1. Substitute k = 1 into the formula to find the first term: 3(1) - 8 = -5.
2. Substitute k = 12 to find the last term: 3(12) - 8 = 36 - 8 = 28.
3. The upper limit is 12, so there are 12 terms.
4. Substitute into S_n = n(a_1 + a_n)/2 to get S_12 = 12(-5 + 28)/2.
5. That is 12(23)/2 = 276/2 = 138.
6. Forgetting the -8 when finding the first term would give a_1 = 3 and a sum of 186, so both endpoints must come from the same formula.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.4 Series and Their Notations_
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