Question

A sequence is defined recursively as follows: a(1) = 1, and a(n)= a(n-1)+n
(a) How do you interpret this recursive rule?

b) Write down the rule for a(2),a(3), and a(4)
it down in your own words.
and determine their values.

Answer 1

Answer:

Step-by-step explanation:

a) The current term number is added to the previous term to get the current term.

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b) Using n = 2, 3, 4 in the given formula, we have ...

  a2 = a1 +2 = 1 +2 = 3

  a3 = a2 +3 = 3 +3 = 6

  a4 = a3 +4 = 6 +4 = 10

The value of the current term is the sum of all positive integers up to the term number, that is, term n is the n-th "triangle number."