Write the terms a 1a1, a 2a2, a 3a3, and a 4a4 of the following sequence. If the sequence appears to converge, make a conjecture about its limit. If the sequence diverges, explain why. a Subscript n Baseline equals StartFraction (negative 1 )Superscript n plus 1 Over 5 n minus 4 EndFractionan= (−1)n+1 5n−4 What are the first four terms of the sequence? a 1a1equals= nothing a 2a2equals= nothing a 3a3equals= nothing a 4a4equals= nothing (Type integers or simplifed fractions.) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

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cristhiansanchez94 cristhiansanchez94 · Answer 1 · 2020-05-01T03:29:21+02:00

Answer:

Step-by-step explanation:

WE are given that [tex]a_n = \frac{(-1)^{n+1}}{5n-4}[/tex]. Then, to now the first for terms, we must replace n by 1,2,3,4 respectively. Then

[tex]a_1 = \frac{(-1)^2}{5(1)-4} = \frac{1}{1}= 1 [/tex]

[tex]a_2 = \frac{(-1)^3}{5(2)-4} = \frac{-1}{6} [/tex]

[tex]a_3 = \frac{(-1)^4}{5(3)-4} = \frac{1}{11}= 1 [/tex]

[tex]a_4 = \frac{(-1)^5}{5(4)-4} = \frac{-1}{16}= 1 [/tex]

Note that as n increase, [tex]a_n[/tex] gets closer to 0. So, the limit of this sequence is 0.