Answer:
see explanation
Step-by-step explanation:
The nth term of an arithmetic sequence is
• [tex]a_{n}[/tex] = a₁ + d(n - 1)
a₁ is the first term , d the common difference , n the term position
(1)
5 , 12 , 19 , 26
a₁ = 5 , d = a₂ - a₁ = 12 - 5 = 7 , then nth term is
[tex]a_{n}[/tex] = 5 + 7(n - 1) = 5 + 7n - 7 = 7n - 2
[tex]a_{n}[/tex] = 7n - 2
To find a₁₁ , substitute n = 11 into [tex]a_{n}[/tex]
a₁₁ = 7(11) - 2 = 77 - 2 = 75
(2)
33 , 28 , 23 , 18
a₁ = 33 , d = a₂ - a₁ = 28 - 33 = - 5 , then nth term is
[tex]a_{n}[/tex] = 33 - 5(n - 1) = 33 - 5n + 5 = - 5n + 38
[tex]a_{n}[/tex] = - 5n + 38
To find a₁₈ , substitute n = 18 into [tex]a_{n}[/tex]
a₁₈ = - 5(18) + 38 = - 90 + 38 = - 52
