Find the 100th term in the sequence 3, 7, 11, 15...

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To answer this question, we need to form an equation to work out the nth term of the series. 

To do this, the first thing we do is calculate the difference between each term.

7 - 3 =4

11 - 7 = 4

15 - 11 = 4

The difference each time is 4. Therefore, the equation could be 4n. Let's try it out with the first term. 

4n = 4 x 1 = 4 which is not equal to the first term, 3. 

To get 3 from the equation we have at the moment, we need to subtract 1. 

Let's try the second term with the equation 4n -1. 

4n-1 = 4x2 -1 = 7 which is equal to the second term. 

To double check that we're right, let's use the equation to calculate the 5th term.

4n -1 = 4x5 -1 = 19. 

19 is 4 greater than 15, so we're right!

Now let's calculate the 100th term. 

4n -1 = 4x100 -1 = 399

Therefore the 100th term of this sequence is 399

Melissa P. GCSE Maths tutor, 13 plus  Maths tutor, 11 Plus Maths tuto...

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