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The first term of an arithmetic sequence is 42. The rule an = an-1 + 8 can be used to find the next term of the sequence.


Explain how to write the explicit rule for the arithmetic sequence from the given information

Respuesta :

The rule shows that each term is 8 more than the previous term, so the common difference is 8.The explicit formula of an arithmetic sequence is the initial term plus (n – 1)d.The explicit rule for this function can be found by substituting 42 for a1 and 8 for d.The explicit rule for the sequence is  42 + (n – 1)8.

MrRoyal

The explicit rule for the arithmetic sequence is: [tex]a_n = 34+ 8n[/tex]

The given parameters are:

[tex]a_1 = 42[/tex] --- the first term

[tex]a_n = a_{n -1} + 8[/tex] --- the recursive rule

Start by calculating a2

[tex]a_2 = a_{2 -1} + 8[/tex]

[tex]a_2 = a_1 + 8\\[/tex]

So we have:

[tex]a_2 = 42 + 8 = 50[/tex]

Calculate the common difference

[tex]d = a_2 - a_1[/tex]

[tex]d = 50 - 42[/tex]

[tex]d = 8[/tex]

The explicit rule, is then calculated as:

[tex]a_n = a_1 + (n - 1)d[/tex]

This gives

[tex]a_n = 42 + (n - 1)8[/tex]

Expand

[tex]a_n = 42 -8+ 8n[/tex]

[tex]a_n = 34+ 8n[/tex]

Hence, the explicit rule for the arithmetic sequence is: [tex]a_n = 34+ 8n[/tex]

Read more about arithmetic sequence at:

https://brainly.com/question/15736659

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