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The first four terms of a sequence are given

$$ \frac{2}{1 \times 2} ;  \frac{2}{2 \times 3} ;  \frac{2}{3 \times 4} ;  \frac{2}{4 \times 5} $$

  1. Write down the next two terms of the sequence
  2. Determine the nth term of the sequence.
  3. Use the answer in the previous question to calculate n if the nth term is $\frac{1}{66}$
in Mathematics by Diamond (60,576 points) | 79 views

1 Answer

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1. 2/(5 x 6) ; 2/(6 x 7)

2. 2/(n-1)(n-2)

3. 2/(n-1)(n-2) = 1/66  , then expand and solve for n,

n^2 -3n -130=0

 (n-13)(n+10)=0

   n= 13 or -10

but n be positive, n=13
by Diamond (42,256 points)

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