Question

Which recursive formula describes the patterns in the perimeter of the images?

A. an=an-1+2;a1=1
B. an=an-1+1;a1=1
C. an=an-1+2;a1=4
D. an=2an-1+1;a1=4

Answer 1

perimiters
adds 2 each time
starts with 4
so
an=4+2(n-1)



a1=4 so it is C or D

answer is C because it increases by 2 each time

Answer 2

Option C is correct.

`a_n =a_(n-1)+2`

`a_1 =4`

Explanation:

The arithmetic sequence says that:

For any sequence
`a_1, a_2, a_3, .....`

the recursive formula for this sequence is given by:

`a_n =a_(n-1)+d`

where d represents the common difference of two consecutive terms and n is the number of terms.

Give the pattern in the figure:

for n = 1,
`a_1 =4`

for n = 2,
`a_2 =6`

for n = 3,
`a_3 =8`

`d =a_2-a_1 =6-4 = 2` or

`d =a_3-a_2 =8-6= 2`

Now, substitute d =2 in the above formula we get;

`a_n=a_(n-1)+2`

Therefore, recursive formula describes the patterns in the perimeter of the images is:

`a_n=a_(n-1)+2`

`a_1 = 4`