College

3-4: MathXL for School Practice & Problem-solving

Part 1 of 2

Write a recursive formula and an explicit formula for the following arithmetic sequence:
\[ 2, 10, 18, 26, 34, \]

A recursive formula is:
\[ a_n = a_{n-1} + 8, \quad a_1 = 2 \]

An explicit formula is:
\[ a_n = 2 + (n-1) \cdot 8 \]

(Simplify your answers.)

Answer :

Final answer:

The arithmetic sequence has a recursive formula of an = an-1 + 8 and an explicit formula of an = 8n - 6.


Explanation:

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, the difference between consecutive terms is 8 (10 - 2 = 8).

To find the recursive formula, we can observe that each term is obtained by adding 8 to the previous term. So, we can write the recursive formula as:

an = an-1 + 8

To find the explicit formula, we can start with the first term and notice that each term can be obtained by multiplying the term number n by 8 and subtracting 6. So, the explicit formula is:

an = 8n - 6


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https://brainly.com/question/35880655


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