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How to find the Nth term for any sequence?

User RaphC
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2 Answers

1 vote

You need to look out for patterns or the rule, like addition, subtraction, multiplication and division. For example:

4, 9, 14, 19, __, __.

Now we need to check for a pattern. In this case we can subtract the first two terms to see, 9 - 4 = 5.

Now we need to see if it lines up with the rest.

5 + 14 = 19.

It does. So when we add 5 with 19, we'll get 24. Adding 5 to that, we get 29, and so on.

Keep in mind the number won't necessarily align when it comes to multiplication and division.

2. 10, 5, 0, -5, -10.

Here we see the same thing. 10 - 5 = 5. So on.

3. 2, 6, 18, 54.

There are big gaps in the numbers, so we will look for multiplication. What multiplies with 2 to make 6? So on.

4. 81, 27, 9, 3.

Look for division, since it's bigger to smaller. What divides 81 to make 27?

Some questions might have a unique sequence, like 1, 2, 4, 7, 11, where the rule is 1, 2, 3, 4.

So in the end, just look out for the rules and line the rule up with all the terms to see what you're dealing with.

User Manish Srivastava
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8.6k points
2 votes

Answer: The formula for the nth term in an arithmetic sequence is an=a1+(n−1)d. This formula can be used to determine the value of any term in an arithmetic sequence. An arithmetic sequence has a common difference between every term.

Hope this helps ✌️

User Sigpwned
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