A1=12−12,a2=23−13,a3=34−14,a4=45−15 ,a5=56−16. a1=12−12,a2=23−13,a3=34−14,a4=45−15 ,a5=56−16. a. find an explicit formula for anan: . b. determine whether the sequence is convergent or divergent: . (enter "convergent" or "divergent" as appropriate.) c. if it converges, find limn→∞an=limn→∞an= .

Clearly, the general for the -th term is



(Aside: given the simple pattern, it's curious why the terms would be given the way they are. It's easier to divine from , but that's just my opinion.)

The sequence does not converge. As , so does .

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

when multiplying or dividing by a negative on both sides you have to flip the inequality sign. this rule only applies to multiplying or dividing by a negative number in inequality equations. this rule is really important.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.