The recursive formula to find nth term of sequence is:
[tex]a_n = 4n - 1 \text{ where } n \geq 1[/tex] and n = 1, 2, 3, ....
Solution:
Given a sequence is:
3, 7, 11, 15, 19, 23, 27, 31, 35
Let us find the difference between terms
7 - 3 = 4
11 - 7 = 4
15 - 11 = 4
19 - 15 = 4
23 - 19 = 4
27 - 23 = 4
31 - 27 = 4
35 - 31 = 4
Thus the difference between terms is constant
Thus the given sequence is arithmetic sequence
An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant
The nth term of arithmetic sequence is given by:
[tex]a_n =a_1+(n-1)d[/tex]
[tex]a_n[/tex] = the nᵗʰ term in the sequence
[tex]a_1[/tex] = the first term in the sequence
d = the common difference between terms
Here in the given sequence
d = 4
[tex]a_1=3[/tex]
Substitute in above formula,
[tex]a_n = 3 + (n-1)(4)\\\\a_n = 3 + 4n - 4\\\\a_n = 4n - 1[/tex]
Thus the recursive formula to find nth term of sequence is:
[tex]a_n = 4n - 1 \text{ where } n \geq 1[/tex] and n = 1, 2, 3, ......
