Post on 26-Dec-2015
State whether the sequence below is arithmetic, geometric or neither and then write the explicit definition of the sequence.
3, 7, 11, 15...
•Arithmetic
•tn = 4n - 1
3, 7, 11, 15...
State whether the sequence below is arithmetic, geometric or neither and then write the explicit definition of the sequence.
3, 6, 11, 18 ...
•Neither
3, 6, 11, 18...
(It’s exponential)
If you subtract 2 from each you have...
1, 4, 9, 16...
Therefore, tn = n²Therefore, tn = n²+2Therefore, tn = n²+2
1, 4, 9, 16...3, 6, 11, 18...
If t3 = 10 and t5 = 16 in an arithmetic sequence, what is t2?
Hint: Find what d equals.
If t3 = 10 and t5 = 16 in an arithmetic sequence, what is t2?
We could make t1 = 10 and t3 = 16 to find d?
tn = t1 + d(n - 1)
16 = 10 + d(3 - 1)
d = 3
If t3 = 10 and t5 = 16 in an arithmetic sequence, what is t2?
d = 3
__, __, 10, __, 16, ... __, __, 10, 13, 16, ... __, 7, 10, 13, 16, ... 4, 7, 10, 13, 16, ...
t2 =
4, 7, 10, 13, 16, ...
t2 = 7
Find the sum of the following infinite geometric series.
8 + 2 + ½+...
r = ¼
8 + 2 + ½+...
t1
1 - rS =
8
1 - ¼S =
S =323
or 102
3
Be sure to review limits and mathematical induction!!!