Question

Can someone please explain this to me!

For the sequence an = 3 + 6 · (n − 1),
its first term is :
its second term is:
its third term is:
its fourth term is:
its fifth term is:
its common difference d=​

Answer 1

`a_n` 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
`a_n-a_(n-1)`. 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,

`a_n-a_(n-1)=(3+6\cdot(n-1)) - (3+6\cdot(n-2))=6\cdot((n-1)-(n-2))=6`