The recursive rule that best describes the sequence 3, 14, 36, 80, ...is [tex]a_{n} =2a_{n-1} +8[/tex].
What is a sequence?
A sequence is a particular order in which related things follow each other.
Let us cross-check the recursive rule [tex]a_{n} =2a_{n-1} +8[/tex]....(1)
Given sequence is: 3, 14, 36, 80, .....
Put n=1, 2, 3 in (1)
[tex]a_{2} =2a_1+8\\a_{2} =2*3+8\\a_{2} =14[/tex]
[tex]a_{3} =2a_2+8\\a_{3} =2*14+8\\a_{3} =36[/tex]
[tex]a_{4} =2a_3+8\\a_{4} =2*36+8\\a_{4} =80[/tex]
We are getting the sequence as 3, 14, 36, 80, ..... i.e. same as the given sequence.
Therefore, the recursive rule that best describes the sequence 3, 14, 36, 80, ...is [tex]a_{n} =2a_{n-1} +8[/tex].
To get more about sequence visit:
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