Answer:
The only common term is 33.
Step-by-step explanation:
We are given the following in the question:
Sequence 1:
[tex]n^{th}\text{ term: } 2n^2 + 1[/tex]
Sequence 2:
[tex]n^{th}\text{ term: } 65 - 2n^2[/tex]
Equating the two terms, we get,
[tex]2n^2 + 1 = 65 - 2n^2\\4n^2 = 64\\\\n^2 = \dfrac{64}{4}\\\\n^2 = 16\\n = \pm 4[/tex]
Since, n cannot take a negative value, we get n = 4.
Thus, there is only 1 common term both the series have for n = 4.
Common term:
[tex]2(4)^2+ 1 - 65-2(4)^2 = 33[/tex]
Thus, the only common term is 33.
