State whether the sequence below is arithmetic, geometric or neither and then write the explicit definition of the sequence. 3, 7, 11, 15...

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Presentation transcript:

State whether the sequence below is arithmetic, geometric or neither and then write the explicit definition of the sequence. 3, 7, 11, 15...

3, 7, 11, 15... Arithmetic tn = 4n - 1

State whether the sequence below is arithmetic, geometric or neither and then write the explicit definition of the sequence. 3, 6, 11, 18 ...

If you subtract 2 from each you have... 3, 6, 11, 18... (It’s exponential) Neither If you subtract 2 from each you have... 3, 6, 11, 18... 1, 4, 9, 16... 1, 4, 9, 16... Therefore, tn = n² Therefore, tn = n²+2 Therefore, tn = n²+2

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? __, __, 10, 13, 16, ... __, __, 10, __, 16, ... __, 7, 10, 13, 16, ... 4, 7, 10, 13, 16, ... 4, 7, 10, 13, 16, ... t2 = 7 t2 =

Find the sum of the following infinite geometric series. 8 + 2 + ½+...

8 + 2 + ½+... r = ¼ t1 1 - r S = 8 1 - ¼ S = S = 32 3 or 10

Be sure to review limits and mathematical induction!!!