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Answer:
A) The first 4 terms of the sequences are: ,
,
and
.
B) An explicit formula for this sequence can be written as:
C) A recursive formula for this sequence can be written as:
Step-by-step explanation:
A) You can find the firs terms of this sequence simply selecting an odd integer and summing the consecutive 3 ones:
(a.1)
B) Observe the sequence of odd numbers 1, 3, 5, 7, 9, 11, 13(...).
You can express this sequence as:
(b.1)
If you merge the expression b.1 in a.1, you obtain the explicit formula of the sequence:
(a.1)
(b.2)
(b.3)
(b.s)
C) The recursive formula has to be written considering an initial term and an N term linked with the previous term. You can see an addition of 8 between a term and the next one. So you can express each term as an addition of 8 with the previous one. Therefore, if the first term is 16:
(c.s)