Question

Given a sequence is defined by the explicit definition LaTeX: t_n=\:n^2+nt n = n 2 + n, find the 4th term of the sequence. (ie LaTeX: t_4t 4)

Answer 1

Answer:

3,5,9,17,33

Step-by-step explanation:

The explicit definition is;

$t_n= {2}^{n} + 1$

When n=1, we get:

$t_1= {2}^{1} + 1 = 2 + 1 = 3$

When n=2, we obtain:

$t_2= {2}^{2} + 1 = 4 + 1 = 5$

When n=3, we get:

$t_3= {2}^{3} + 1 = 8+ 1 = 9$

When n=4, we get:

$t_4= {2}^{4} + 1 = 16 + 1 = 17$

When n=5, we obtain:

$t_5= {2}^{5} + 1 = 32 + 1 = 33$

The sequence generated is 3,5,9,17,33,...

The third choice is correct.

Answer 2

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