Sequences Revision 2
By Rhys Sutton
Arithmetic sequences An Arithmetic
sequence also called arithmetic progression, is a sequence that increases or decreases by the same each time Example 1, 4, 7, 10, 13 – This is increasing by 3 each time 5, 2.5, 0, -2.5, -5 This is decreasing by -2.5 each time
If
the sequence is increasing by 3 each time then you write that as Ur + 1 = Ur + d d is the common difference so d is 3 Ur + 1 = Ur + 3
To check you can just change r to one of the terms 1, 4, 7, 10, 13 Ur + 1 = Ur + 3 1 is the 1st term, 4 is the 2nd and so on. To check the 2nd term put r as 4 U4 + 1 = U4 + 3 So U5 = 7
When
you need to find a term you use
this Ur = a + (r-1)d a is the 1st term in the sequence And again d is the common difference So if you where given a = 2 and d = 3 and want to find the 5th term then U5 = 2 + (5-1)3 = 2+12 = 14 So the 5th term is 14
Arithmetic sequences An Arithmetic
sequence also called arithmetic progression, is a sequence that increases or decreases by the same each time Example 1, 4, 7, 10, 13 – This is increasing by 3 each time 5, 2.5, 0, -2.5, -5 This is decreasing by -2.5 each time
If
the sequence is increasing by 3 each time then you write that as Ur + 1 = Ur + d d is the common difference so d is 3 Ur + 1 = Ur + 3
To check you can just change r to one of the terms 1, 4, 7, 10, 13 Ur + 1 = Ur + 3 1 is the 1st term, 4 is the 2nd and so on. To check the 2nd term put r as 4 U4 + 1 = U4 + 3 So U5 = 7
When
you need to find a term you use
this Ur = a + (r-1)d a is the 1st term in the sequence And again d is the common difference So if you where given a = 2 and d = 3 and want to find the 5th term then U5 = 2 + (5-1)3 = 2+12 = 14 So the 5th term is 14
