Let a1, a2, a3,...
an,... be a sequence of positive
numbers. The first five terms of the sequence are given below.
8, 11, 17, 26, 38, ...
Select the correct rule for finding the (n+1)th term from the
nth term.
an+1 = an + 3
an+1 = nan
an+1 = an + 3n
an+1 = an + 8
an+1 = an + 12
1
Sorry, that's not right. For an = 8, the expression you selected evaluates as: 8 + 3 = 11. The next term is 11, so the rule works for these particular numbers. But it does not work in general. For example, when an = 11, 11 + 3 = 14. But the next term in the sequence is 17, not 14, so the rule fails in this case. It's a good approach to test your rule by checking it with several pairs of numbers from the sequence.
Student answered incorrectly.
2
Sorry, that's not right. Think about the following example: The first term is 8, so when n = 1, an = 8. 1 * 8 = 8. But the next term in the sequence is 11, not 8. So this rule does not apply to the sequence given in the question. It's a good approach to test your rule by checking it with several pairs of numbers from the sequence.
Student answered incorrectly.
3
The expression you selected is correct. Great job!
The student answered correctly.
4
Sorry, that's not right. For an = 8, the expression you selected evaluates as: 8 + 8 = 16. But the next term in the sequence is 11, not 16. So this rule does not apply to the sequence given in the question. It's a good approach to test your rule by checking it with several pairs of numbers from the sequence.
Student answered incorrectly.
5
Sorry, that's not right. For an = 26, the expression you selected evaluates as: 26 + 12 = 38. The next term is 38, so the rule works for these particular numbers. But it does not work in general. For example, when an = 11, 11 + 12 = 23. But the next term in the sequence is 17, not 23, so the rule fails in this case. It's a good approach to test your rule by checking it with several pairs of numbers from the sequence.
Student answered incorrectly.
RecursiveRuleOther