Question

1 a) is the above sequence arithmetic? Justify your answer. b) Write the explicit formula for the above sequence. c) Find the 18th term.

Answer 1

First, we count the number of boxes.

We have: 4,8,12,16

(a)Now:

• 8-4=4

,

• 12-8=4

,

• 16-12=4

Since the difference is the same, the sequence is an arithmetic sequence.

(b)In the sequence

First term, a =4

Common difference, d=4

The nth term of an arithmetic sequence is:

`\begin{gathered} U_n=a+(n-1)d \\ =4+4(n-1) \\ =4+4n-4 \\ =4n \end{gathered}`

The explicit formula for the above sequence, f(n)= 4n.

(c)18th term

f(18)= 4 x 18

=72

The 18th term is 72.