Write the rule for the nth term given −1/2,−1/4,−1/6,−1/8,...

potrefilizx

potrefilizx

Answered question

2022-09-04

Write the rule for the nth term given - 1 2 , - 1 4 , - 1 6 , - 1 8 , ...

Answer & Explanation

Everett Melton

Everett Melton

Beginner2022-09-05Added 12 answers

It is observed in the sequence that while numerator is constant at −1, the difference between the denominator of a term of the sequence to the denominator of its preceding term is constant at 2, as denominators are {2,4,6,8,..........}.
Clearly, it is not the sequence but its denominators, which are in arithmetic sequence {2,4,6,8,..........}, with first term as 2 and common difference at 2.
As the n t h of a sequence whose first term is a and common difference is d is a+(n−1)d, n t h of the sequence {2,4,6,8,..........} is
2 + ( n - 1 ) × 2 = 2 + 2 n - 2 = 2 n
Hence nth of the sequence { - 1 2 , - 1 4 , - 1 6 , - 1 8 , ... ... ... . } is - 1 2 n

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