Write a recursive formula to represent the sequence below.
(3,7, 11, 15, 19,23,27,31,35,

The recursive formula to find nth term of sequence is:

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:

= the nᵗʰ term in the sequence

= the first term in the sequence

d = the common difference between terms

Here in the given sequence

d = 4

Substitute in above formula,

Thus the recursive formula to find nth term of sequence is:

and n = 1, 2, 3, ......

yes

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step-by-step explanation: