Sequences

Sequences

- July 02, 2020

Here are some sequences for you to find the nth term in:

11, 18, 25, 32

2, 5, 10, 17, 26

5, 11, 21, 35

12, 19, 26, 33

14, 28, 50, 80

Comments

Yash2 July 2020 at 12:19
1. 7n + 4
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Anonymous3 July 2020 at 07:34
Yes Yash you are corect
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Anonymous3 July 2020 at 07:59
Yash has already answered the first one but I'll explain why.

if you look at the gap between each number in the sequence, you will see it is 7. now add an n on 7 and then do 11 - 7 because 11 is the first term and when you look at the first term, n is 1. Second term n is 2 and so on. So, the 11 - 7 is 4 so you will have 7n + 4.

Now for question 2:
For quadratic sequences, there is something called the first and second difference. To solve the quadratic sequence, you will need the 2nd difference - which you will only get by using the first difference. Here is how you do it.

Sequence: 2, 5, 10, 17, 26
First difference: +3, +5, +7, +9
second difference: +2, +2, +2

As you may have spotted, the second difference is the same. Now you now the second difference, you take that number half it and add an n^2 (n squared) to it. So in this case it would just become n squared. then you take the n squared and think of what the sequence would be. Well it would just be 1, 4, 9, 16, 25. The square numbers. You then get the first sequence and minus it off the square number sequence. which would give you 1, 1, 1, 1, 1 so that sequence's nth term would be 1. now you just add that to the n squared which would give you n squared + 1.

Now that I've told you that, you can solve the others.

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