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Algebra

Algebra. n th Term. Algebra. When we are working to find the n th term we are looking to find patterns in number sequences. Algebra. 25,. 29,. Look at this sequence of numbers: 5, 9, 13, 17, 21, …, …, What are the next two numbers in the sequence?. Algebra. 25,. 29,.

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Algebra

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  1. Algebra nth Term

  2. Algebra When we are working to find the nth term we are looking to find patterns in number sequences.

  3. Algebra 25, 29, Look at this sequence of numbers: 5, 9, 13, 17, 21, …, …, What are the next two numbers in the sequence?

  4. Algebra 25, 29, What would the 10th number be? 5, 9, 13, 17, 21, …, …, How can we know without the 8th and 9th numbers..?

  5. Algebra We need to be able to use the ‘place’ value of each number (the nth term) 1 2 3 4 5 6 7 5, 9, 13, 17, 21, 25, 29

  6. Algebra Now look at each number in the sequence. What is the difference between each number? 1 2 3 4 5 6 7 5, 9, 13, 17, 21, 25, 29 4 4 4 4 4 4

  7. Algebra This difference tells us how much we need to multiply the nth term by. 1 x 4 = 4 1 2 3 4 5 6 7 5, 9, 13, 17, 21, 25, 29 4 4 4 4 4 4

  8. Algebra But the sequence number is 5, not 4! OK, then just add 1 as well 1 x 4 = 4 4 +1= 5 1 2 3 4 5 6 7 5, 9, 13, 17, 21, 25, 29 4 4 4 4 4 4

  9. Algebra We know n has to be multiplied by 4, add 1 Now try it on another n… 6? 6 x 4 = 24 24 +1= 25 1 2 3 4 5 6 7 5, 9, 13, 17, 21, 25, 29 4 4 4 4 4 4

  10. Algebra So our rule for finding any number in this sequence is… 4n + 1 1 2 3 4 5 6 7 5, 9, 13, 17, 21, 25, 29 4 4 4 4 4 4

  11. Algebra When answering a question is it really important to present it so that it is really clear. Draw a small table to show both the sequence and the term place values…

  12. Algebra 3 3 3 3 3 3 Difference between numbers is 3 Term 1 is multiplied by 3 then subtract 1 = 2 = 3n-1 4th term 4 x 3 - 1 = 11

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