Question 1121858: The following are defined using recursion formulas. Write the first four terms of each sequence.
a1 = 7 and an = an-1 + 5 for n ≥ 2
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
A recursive formula tells you how to build the sequence by giving you the first number, or the first few numbers, and telling you how to find each later number in the sequence from the earlier ones.
Let me revise the notation a bit so it is easier to understand.
(1) a(1) = 7
This tells you the first term of the sequence ("a sub 1") is 7.
(2) a(n) = a(n-1)+5 for n greater than or equal to 2
This tells you that each term ("a sub n") is 5 more than the preceding term ("a sub (n-1)").
So term 2 ("a sub 2") is 5 more than term 1 ("a sub (2-1)"; i.e., "a sub 1")
So a(2) = a(1)+5 = 7+5 = 12.
Then the recursive formula tells you the 3rd term is 5 more than the 2nd; and that the 4th term is 5 more than the 3rd; and so on.
So the sequence is
7, 12, 17, 22, 27, 32, 37, ...
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