How do you write the expression for the nth term of the sequence given −2/3,3/4,−4/5,5/6,−6/7,...?

Presley Esparza

Presley Esparza

Answered question

2022-09-14

How do you write the expression for the nth term of the sequence given - 2 3 , 3 4 , - 4 5 , 5 6 , - 6 7 , ... ?

Answer & Explanation

ivice7u

ivice7u

Beginner2022-09-15Added 18 answers

Let us divide this in three parts.
First - Numerator goes like {2,3,4,5,6,..}. Here, we have arithmetic sequence with first term is 2 and common difference as 1 and hence a n = 2 + ( n - 1 ) × 1 = n + 1
Second - Denominator goes like {3,4,5,6,7,..}. Here, we have arithmetic sequence with first term is 3 and common difference as 1 and hence a n = 3 + ( n - 1 ) × 1 = n + 2
Third - The sign of every odd term is minus and every even term is plus and we can say that this is given by ( - 1 ) n
Hence, we can write the expression for the n t h term of the sequence as
a n = ( - 1 ) n n + 1 n + 2

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