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The second term of an arithmetic sequence is –39. The rule mc014-1.jpg can be used to find the next term of the sequence. What is the explicit rule for the arithmetic sequence?

Answer :

HomertheGenius
a 2 = -39
a 2 = a 1 + 12
- 39 = a 1 + 12
a 1 = - 39 - 12
a 1 = - 51 ( first term )
The common difference is : d = 12
The explicit rule for the arithmetic sequence:
a n = a1 + ( n - 1 ) d
a n = -51 + ( n - 1 ) · 12 
Lanuel

The explicit rule for this arithmetic sequence is [tex]a_n = -51 +(n-1)12[/tex]

Given the following data:

  • Second term = -39.
  • Common difference = 12.

To determine the explicit rule for the arithmetic sequence:

How to calculate an arithmetic sequence.

Mathematically, an arithmetic sequence is given by the expression:

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

Where:

  • d is the common difference.
  • [tex]a_1[/tex] is the first term of an arithmetic sequence.
  • n is the total number of terms.

Substituting the given parameters into the formula, we have;

[tex]-39 = a_1 +(2-1)12\\\\-39=a_1+12\\\\a_1=-39-12\\\\a_1=-51[/tex]

For the explicit rule:

[tex]a_n = -51 +(n-1)12[/tex]

Read more on arithmetic sequence here: brainly.com/question/12630565

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