Given the sequence is defined by the explicit definition LaTeX: t_n=2^n-nt n = 2 n − n, find the 5th term of the sequence. (ie LaTeX: t_5t 5)
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Answer:
[tex]t_{5}=27[/tex]
Step-by-step explanation:
Given:
The [tex]n^{th}[/tex] term of the sequence is given as:
[tex]t_{n}=2^{n}-n[/tex]
In order to find the fifth term of this sequence, we need to plug in 5 for [tex]n[/tex] in the above expression and solve. This gives,
[tex]t_{5}=2^{5}-5\\t_{5}=32-5=27[/tex]
Therefore, the fifth term of the sequence is [tex]t_{5}=27[/tex].