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)

Given the sequence is defined by the explicit definition LaTeX tn2nnt n 2 n n find the 5th term of the sequence ie LaTeX t5t 5 class=

Respuesta :

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].

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