An arithmetic sequence is defined by the recursive formula t1 = 11, tn = tn - 1 - 13, where n ∈N and n > 1. Which of these is the general term of the sequence? A) tn = 11 - 13 (n - 1), where n ∈N and n > 1 B) tn = 11 - 13 (n - 2), where n ∈N and n ≥ 1 C) tn = 11 - 13 (n - 1), where n ∈N and n ≥ 1 D) tn = 11 - 13 (n + 1), where n ∈N and n ≥ 1

Question

Samuel Benton

Mathematics

11 December, 01:42

An arithmetic sequence is defined by the recursive formula t1 = 11, tn = tn - 1 - 13, where n ∈N and n > 1. Which of these is the general term of the sequence? A) tn = 11 - 13 (n - 1), where n ∈N and n > 1 B) tn = 11 - 13 (n - 2), where n ∈N and n ≥ 1 C) tn = 11 - 13 (n - 1), where n ∈N and n ≥ 1 D) tn = 11 - 13 (n + 1), where n ∈N and n ≥ 1

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Answers (1)

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Grayson Stewart · Answer 1

The answer is C) tn = 11 - 13 (n - 1), where n ∈N and n ≥ 1

In the recursive formula, - 13 is the common difference, while 11 is the first term t ₁. The explicit form of this sequence is given by tn = t₁ + d (n-1); where d is the common difference.

It is also important to note that 1 can now be substituted to n (unlike the recursive formula). This means that you are finding the 1st term of the sequence. Substituting 1, you will get 11 which satisfies the original statement.