1. Find a formula for the general term of the sequence, assuming the pattern continues and that the first term corresponds to , 2. Determine whether the sequence converges or diverges. If it converges, find its limit. 3. Determine whether each series is convergent or divergent. If it is convergent, find its sum.

  1. an = (-1)^(n-1)·(n+2)!/3^n

  2. the sequence diverges

Step-by-step explanation:

Perhaps you're concerned with the sequence ...

  {2, -24/9, 120/27, -720/81, ...}

1. This is neither arithmetic nor geometric. Ratios of terms are -4/3, -5/3, -6/3.

The alternating signs mean one factor of the general term is (-1)^(n-1). The divisors of 3 in the term ratios indicate 3^-n is another factor. The increasing multipliers suggest that a factorial is involved.

If we rewrite the sequence factoring out (-1)^(n-1)/3^n, we have ...

  {6, 24, 120, 720, ...}

corresponding to 3!, 4!, 5!, 6!. This lets us conclude the remaining factor is (n+1)!.

The general term is ...

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2. The magnitude of the factorial quickly outstrips the magnitude of the exponential denominator, so the terms keep getting larger and larger.

The sequence diverges.

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3. No series are provided.

we'll this would mean that the dunk tank and the bounce house are the same for 20 hours because the 2 represents that the two activities, and the 20 represents the amount of hours they both are. so with this said, it means that the answer is c. the costs for a dunk tank and bounce house are the same for 20 hours.

c.the costs for a dunk tank and bounce house are the same for 20 hours.

hope this .

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?