Question

A sequence has the following terms, a_(3)=16,a_(4)=23, a_(5)=30, and a_(7)=44. Which of the following can be used to find the nth term of the sequence?

Answer 1

To find the nth term of a sequence, determine the pattern or rule that governs the sequence and use the formula an = a1 + (n - 1)d, where a1 is the first term, d is the common difference, and n is the position of the term.

Step-by-step explanation:

To find the nth term of a sequence, we need to find the pattern or rule that governs the sequence. In this case, we have the following terms: a3 = 16, a4 = 23, a5 = 30, and a7 = 44. Looking at the sequence, we can see that each term is obtained by adding 7 to the previous term. Therefore, the nth term of the sequence can be found using the formula an = a1 + (n - 1)d, where a1 is the first term, d is the common difference between terms, and n is the position of the term.

For this sequence, the first term a1 is 16 and the common difference d is 7. Plugging these values into the formula, we get an = 16 + (n - 1)7. This formula can be used to find any term in the sequence.

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