Question

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.

Answer 1

Answer:

Step-by-step explanation:

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

$a_1 = \frac{(-1)^2}{5(1)-4} = \frac{1}{1}= 1$

$a_2 = \frac{(-1)^3}{5(2)-4} = \frac{-1}{6}$

$a_3 = \frac{(-1)^4}{5(3)-4} = \frac{1}{11}= 1$

$a_4 = \frac{(-1)^5}{5(4)-4} = \frac{-1}{16}= 1$

Note that as n increase, $a_n$ gets closer to 0. So, the limit of this sequence is 0.