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

Explanation:

WE are given that
`a_n = ((-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 = ((-1)^2)/(5(1)-4) = (1)/(1)= 1`

`a_2 = ((-1)^3)/(5(2)-4) = (-1)/(6)`

`a_3 = ((-1)^4)/(5(3)-4) = (1)/(11)= 1`

`a_4 = ((-1)^5)/(5(4)-4) = (-1)/(16)= 1`

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