Answer:
see explanation
Step-by-step explanation:
The common difference d of an arithmetic sequence is
d = [tex]a_{2}[/tex] - [tex]a_{1}[/tex] = [tex]a_{3}[/tex] - [tex]a_{2}[/tex]
Substitute in values and solve for k, that is
5k - 1 - 2k = 6k + 2 - (5k - 1)
3k - 1 = 6k + 2 - 5k + 1
3k - 1 = k + 3 ( subtract k from both sides )
2k - 1 = 3 ( add 1 to both sides )
2k = 4 ⇒ k = 2
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The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d
[tex]a_{1}[/tex] = 2k = 2 × 2 = 4 and
d = 5k - 1 - 2k = 3k - 1 = (3 × 2) - 1 = 5
Hence
[tex]a_{8}[/tex] = 4 + (7 × 5) = 4 + 35 = 39
