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<em><u>The recursive formula to find nth term of sequence is:</u></em>
and n = 1, 2, 3, ....
<em><u>Solution:</u></em>
Given a sequence is:
3, 7, 11, 15, 19, 23, 27, 31, 35
<em><u>Let us find the difference between terms</u></em>
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
<em><u>The nth term of arithmetic sequence is given by:</u></em>
= 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,
<em><u>Thus the recursive formula to find nth term of sequence is:</u></em>
and n = 1, 2, 3, ......
You want to be finding out what two factors (where one of them is a perfect square) has the produce of 63. It seems like 9 x 7 (9 is the perfect square) works.
The square root of 9 is 3 so we can just have
(which just means 3 times the square root of 7).
The square root of 9 is 3 so we can just have