[tex]a_n[/tex] is the n-th term in the sequence. So
• the first term (n = 1) is a₁ = 3 + 6•(1 - 1) = 3
• the second term (n = 2) is a₂ = 3 + 6•(2 - 1) = 9
• the third term (n = 3) is a₃ = 3 + 6•(3 - 1) = 15
• the fourth term (n = 4) is a₄ = 3 + 6•(4 - 1) = 21
• the fifth term (n = 5) is a₅ = 3 + 6•(5 - 1) = 27
The common difference between terms is what you get from subtracting consecutive terms in the sequence, or the number [tex]a_n-a_{n-1}[/tex]. Just by taking any two consecutive numbers from above, you have d = 6, since
9 - 3 = 6
15 - 9 = 6
and so on. More generally,
[tex]a_n-a_{n-1}=(3+6\cdot(n-1)) - (3+6\cdot(n-2))=6\cdot((n-1)-(n-2))=6[/tex]
