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100 points + Brainliest Please help! Please give steps!!
The sequence one-sixth, negative two-sevenths, three eighths, negative four ninths, and so on is given.
Part A: Assuming the pattern continues, list the next four terms in the sequence. Show all necessary math work. (4 points)
Part B: Write the explicit equation for f (n) to represent the sequence. Show all necessary math work. (4 points)
Part C: Is the sign of f (53) positive or negative? Justify your reasoning mathematically without determining the value of f (53). (2 points)

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sqdancefan

Answer:

  A.  1/2, -6/11, 7/12, -8/13

  B. f(n) = n(-1)^(n-1)/(n+5)

  C. positive

Step-by-step explanation:

You want the next few terms, the general term, and the sign of term 53 for the sequence that begins 1/6, -2/7, 3/8, -4/9, ....

A. Pattern

The numerators are the counting numbers. The denominators are also counting numbers, 5 more than the numerator. The signs of odd-numbered terms are positive. The next 4 terms in the sequence are ...

  5/10 (= 1/2), -6/11, 7/12, -8/13

B. Equation

We know that (-1)^n alternates signs as n increases through the integers. If we want term n=1 to be positive, we can write this factor as (-1)^(n-1).

The equation expressing the above-described general term is ...

  f(n) = n·(-1)^(n-1)/(n+5)

C. Sign

The 53rd term is an odd-numbered term, so will have the same sign as the first term. The sign of f(53) is positive.

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