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Starter Find the next 3 terms of the sequence: 2, 5, 8, 11, … 2, 6, 18, 54 4n – 2 -5n + 3 14, 17, 20 162, 486, 1458 2, 6, 10 -2, -7, -12
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Starter. Find the next 3 terms of the sequence: 2, 5, 8, 11, … 2, 6, 18, 54 4n – 2 -5n + 3. 14, 17, 20. 162, 486, 1458. 2, 6, 10. -2, -7, -12. Note 3: Arithmetic Sequences. The formula for an arithmetic sequence is:. u n = u 1 + (n – 1)d. u 1 = first term - PowerPoint PPT Presentation
Transcript of Starter
StarterFind the next 3 terms of the sequence:
2, 5, 8, 11, …
2, 6, 18, 54
4n – 2
-5n + 3
14, 17, 20
162, 486, 1458
2, 6, 10
-2, -7, -12
Note 3: Arithmetic Sequences An arithmetic sequence is where a number is
added to get the next term The number is called the common difference
The formula for an arithmetic sequence is:
un = u1 + (n – 1)d
u1 = first termd = common difference = un+1 - un un = the nth term
Example 1
Calculate the 24th term in the arithmetic sequence
2, 6, 10, 14, …
u1 = d =
un = u1 + (n – 1)d2 4
u24 = 2 + (24 – 1)4
= 94
Sometimes you may not be asked for a term, but other parts of the formula, requiring rearranging and solving:
Example 2In the sequence 2, 4, 6, 8,….what is term 644?
u1 = d =
un = u1 + (n – 1)d2 2
644 = 2 + (n – 1)x2
n = 322
644 = 2 + 2n - 2644 = 2n
Example 3
Find the formula for the nth term of the sequence
5, 9, 13, 17, …
u1 = d =
un = u1 + (n – 1)d5 4
un = 5 + (n – 1)4
= 5 + 4n - 4
= 4n + 1
Page 436
Exercise 14C
Q 1-6
