Question

Select the correct answer from each drop-down menu.

Answer 1

The explicit formula for an arithmetic sequence is  an = a1 +  d(n - 1)   where a1 is the first term and d = common difference.  For this sequence  a1 is 7 and  d =  13- 7 = 19 - 13 = 25 - 19 = 6

So explicit formula required = 7 + 6(n - 1)

Answer 2

Answer:

Recursive Formula:  f(n)=f(n-1)+6

Explicit formula: f(n)= 6n+1

Step-by-step explanation:

We are given a sequence of arithmetic progression as:

               7 , 13 , 19 , 25

This means that the common difference of the sequence is: 6

(  Since

13-7=6

19-13=6

and 25-19=6 )

This means that each term of the sequence is 6  more than that of the preceding term of the sequence.

i.e.  the recursive formula for the sequence is given by:

            f(n)=f(n-1)+6

Also, the general rule or the explicit function that describes this situation is:

         f(n)=6n+1

(  Since the first term of the sequence is calculated when n=1

f(1)=6×1+1=7

second term i.e. n=2

f(2)=6×2+1=13

f(3)=6×3+1=19

and so on  )