Identify the sequence as arithmetic or geometric, and write a recursive formula for the sequence. be
sure to identify your starting value
49, 7, 1, 1 / 7, 1 / 49, …

The sequence is geometric. The recursive formula is

Step-by-step explanation:

In order to identify if the sequence is arithmetic or geometric, you can calculate the difference and the ratio of two consecutive terms.

If the difference is common for all two consecutive terms,then  the sequence is arithmetic. (The difference of the largest number minus the smallest one)

If the ratio is common for all two consecutive terms, then the sequence is geometric. (The ratio is obtained by dividing a term by the previous term)

Calculating the difference:

-For the first and second terms:

49-7=42

-For the second and third terms:

7-1=6

You can notice that the difference isn't common.

Calculating the ratio:

-For the first and second terms:

7÷49=1/7

-For the second and third terms:

1÷7=1/7

-For the third and fourth terms:

1/7 ÷1 =1/7

Therefore 1/7 is a common ratio and the sequence is geometric.

The recursive formula of a geometric sequence is:

where An is the nth term, An-1 is the previous term and r is the common ratio.

Replacing r=1/7:

An-1 is calculated with:

where a is the first term of the sequence.