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-1, 2, 7, 14, 23

To find the nth term, firstly find the difference between the terms

The difference between -1 and 2 is 3 because -1+3 = 2
Similarly 2 and 7 had difference of 5

7 and 14 has difference of 7
14 and 23 has difference of 9

So the differences are: 3, 5, 7, 9
Now find the difference of the differences  (2nd difference)
It is 2 because you add 2 to 3 to get to 5 and so on.

We know it's a quadratic sequence because the first difference is not all same
So now what you do is you half the second difference which was 2 so it becomes 1 and then multiply 1 with n^2.
This gives us the quadratic part of the sequence but we also need the linear part of the sequence too. So using n^2, generate another sequence 
So first five square numbers 
1, 4, 9, 16, 25 
Subtract  each number of 1, 4, 9, 16, 25 from each number of        -1, 2, 7, 14, 23
You will get                           -2, -2, -2, -2, -2 

So the linear sequence is just -2 

Now combine the quadratic and linear sequence to find the nth term
So the answer is n^2-2 
Here is working out:

                            -1, 2,  7, 14, 23
1st Difference :   3,  5,  7,  9
2nd difference:       2, 2,  2
Half the 2nd difference which will be 1 then multiply by n squared so n^2

Generate another sequence using n^2
 So all square numbers but only need 5

1, 4, 9, 16, 25
Subtract them from
-1, 2, 7, 14, 23
You will get another sequence below
-2, -2, -2, -2, -2

This has -2 in common which means it's just -2 

Therefore, final answer: n^2-2 

Hope that helps.

Maths

The nth term of -1,2,7,14,23

5n-2 is formula to a generate a whole arithmetic sequence. By using this formula you can generate any term of the sequence. So let us do it here.

If I want to work out the 1st term, I would simply put n = 1 in the formula,
 
So 5(1)-2 = 5-2 = 3 so the term term is 3.
So to find the 10th term simply put n =10 

Which is 5(10)-2 = 50-2 =48

Hope this helps!

Find 10th term in a rule 5n - 2

We are gonna solve this using the balance method and using inverse operations. 

So the question is 4-x < 9

First of all you need to get the numbers on the same side of Inequality sign (<), we have a positive 4 so we will do the opposite subtract from both sides 

4 take away 4 gives 0 
9 take away 4 gives 5

So now we will have -x < 5 

We want x the subject but it's negative x so we will multiply both sides with negative -1 

So -1 multiply by -x gives just x 
-1 multiply by 5 is -5 

Because we multiply by a negative the inequality sign will change from < to > 
So the answer is x > -5 

Here is working out:

   4-x < 9
  -4       -4
      -x < 5
multiply both sides by -1 
 Answer: x > 5

Hope this helps.

Malik Nabeel Ahmed

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