The new rule for the reversed term-by-term sequence is : subtract 13, then divide the result by 6.
Steps on how to generate the new rule
In the original sequence of three terms, let
[tex]T_{k-1}=\text{the (k-1)th term}\\T_k=\text{the kth term}[/tex]
The term-by-term rule (multiply by 6 and then add 13
) can be expressed using the formula
[tex]T_k=6T_{k-1}+13[/tex]
If the terms in the sequence are reversed, how do we get the new term-by-term rule?
When the sequence is reversed, we will have [tex]T_k[/tex] coming before [tex]T_{k-1}[/tex]. What we do is to take the previous rule, and make
[tex]T_k=6T_{k-1}+13\\\implies T_k-13=6T_{k-1}\\\\\implies \dfrac{T_k-13}{6}=T_{k-1}[/tex]
Hence we can conclude that The rule for the reversed sequence is : subtract 13, then divide the result by 6.
Learn more about arithmetic sequences here https://brainly.com/question/16130064
