Arithmetic Sequences and Sums
Arithmetic Sequences and Sums
Arithmetic Sequences and Sums
Sums
Sequence
A Sequence is a set of things (usually numbers) that are in order.
Arithmetic Sequence
In an Arithmetic Sequence the difference between one term and the next
is a constant.
In other words, we just add the same value each time ... infinitely.
Example:
Example: (continued)
Has:
And we get:
Rule
xn = a + d(n−1)
(We use "n−1" because d is not used in the 1st term).
Example: Write a rule, and calculate the 9th term, for this
Arithmetic Sequence:
xn = a + d(n−1)
= 3 + 5(n−1)
= 3 + 5n − 5
= 5n − 2
x9 = 5×9 − 2
= 43
So:
Becomes:
Check: why don't you add up the terms yourself, and see if it comes to 145
2S = n × (2a + (n−1)d)