alleryStart learning →Write a recursive formula for the arithmetic sequence -18, -7, 4, 15, 26.
Aa_1 = -18 and a_n = a_(n-1) + 7
Ba_1 = -18 and a_n = a_(n-1) + 11
Ca_1 = -18 and a_n = a_(n-1) - 11
Da_1 = -7 and a_n = a_(n-1) + 11
Answer & Solution
Correct answer: B. a_1 = -18 and a_n = a_(n-1) + 11
1. Subtract the first term from the second: -7 - (-18) = 11.
2. Checking another pair, 4 - (-7) = 11, confirms the sequence is arithmetic with d = 11.
3. A recursive formula also needs its initial term stated, and that is a_1 = -18.
4. So the rule is a_1 = -18 with a_n = a_(n-1) + 11 for n >= 2.
5. Reading the subtraction backwards gives -11, which would send the sequence downward instead of upward.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.2 Arithmetic Sequences_
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