Answer:
Sally is not right
Step-by-step explanation:
Given the two sequences which have their respective [tex]n^{th}[/tex] terms as following:
Sequence A. [tex]3n - 2[/tex]
Sequence B. [tex]10 - 2n[/tex]
As per Sally, there exists only one number which is in both the sequences.
To find:
Whether Sally is correct or not.
Solution:
For Sally to be correct, we need to put the [tex]n^{th}[/tex] terms of the respective sequences as equal and let us verify that.
[tex]3n-2=10-2n\\\Rightarrow 3n+2n=10+2\\\Rightarrow 5n=12\\\Rightarrow n = \dfrac{12}{5}[/tex]
When we talk about [tex]n^{th}[/tex] terms, [tex]n[/tex] here is a whole number not a fractional number.
But as per the statement as stated by Sally [tex]n[/tex] is a fractional number, only then the two sequences can have a number which is in the both sequences.
Therefore, no number can be in both the sequences A and B.
Hence, Sally is not right.
