Question write a recursive formula for the following sequence 25,43,61,79,97 F(1)= 25 F(n)= F (n-1) +18

Given: The sequence is: 25,43,61,79,97 To find: The recursive formula for the given sequence. Solution: We have, 25,43,61,79,97 Here, the first term is 25. Now, the differences between the two consecutive terms are: [tex]43-25=18[/tex] [tex]61-43=18[/tex] [tex]79-61=18[/tex] [tex]97-79=18[/tex] The differences between the two consecutive terms is common, i.e., 18. So, the given sequence is an arithmetic sequence. The recursive formula of an arithmetic sequence is: [tex]F(n)=F(n-1)+d[/tex] Where, d is the common difference and F(1) is the first term. Putting [tex]d=18[/tex], we get [tex]F(n)=F(n-1)+18[/tex], where [tex]F(1)=25[/tex]. Therefore, the required recursive formula is [tex]F(n)=F(n-1)+18[/tex], where [tex]F(1)=25[/tex]. Log in to Reply

Given:The sequence is:

25,43,61,79,97

To find:The recursive formula for the given sequence.

Solution:We have,

25,43,61,79,97

Here, the first term is 25. Now, the differences between the two consecutive terms are:

[tex]43-25=18[/tex]

[tex]61-43=18[/tex]

[tex]79-61=18[/tex]

[tex]97-79=18[/tex]

The differences between the two consecutive terms is common, i.e., 18. So, the given sequence is an arithmetic sequence.

The recursive formula of an arithmetic sequence is:

[tex]F(n)=F(n-1)+d[/tex]

Where, d is the common difference and F(1) is the first term.

Putting [tex]d=18[/tex], we get

[tex]F(n)=F(n-1)+18[/tex], where [tex]F(1)=25[/tex].

Therefore, the required recursive formula is [tex]F(n)=F(n-1)+18[/tex], where [tex]F(1)=25[/tex].