Answer:
d. a_n = 6n - 4.
Step-by-step explanation:
The common difference (d) is 8-2 = 14-8 = 20-14 = 26-20 = 6.
This is an Arithmetic Sequence with the first term (a1) is 2.
The general form of the explicit formula is a_n = a1 + d(n - 1) so this sequence has the formula:
a_n = 2 + 6(n - 1)
a_n = 2 + 6n - 6
a_n = 6n - 4.
The sequence is an illustration of an arithmetic sequence.
The explicit formula is: (d) [tex]a_n = 6n - 4[/tex]
We have:
[tex]a_1 = 2[/tex] -- the first term
Next, we calculate the common difference (d)
[tex]d = a_2 - a_1[/tex]
So, we have:
[tex]d = 8 -2[/tex]
[tex]d = 6[/tex]
The explicit formula is calculated using:
[tex]a_n = a_1 + (n - 1)d[/tex]
So, we have:
[tex]a_n =2 + (n - 1) \times 6[/tex]
Open bracket
[tex]a_n = 2 + 6n - 6[/tex]
Collect like terms
[tex]a_n = 6n - 6 + 2[/tex]
[tex]a_n = 6n - 4[/tex]
Hence, the explicit formula is: (d) [tex]a_n = 6n - 4[/tex]
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