Question

For the following exercises, write an explicit formula for each sequence.

Answer 1

Consider the following sequence,

{0, 1-e1/1 + e1, 1 – e2/1 + e3, 1 – e3/1+e4, 1 – e4/1 + e5, …} ...... (1)

 

Consider the numerators of the terms,

        0 = 1 – 1

           = 1 – e1-1

1 – e1 = 1 – e2-1

1 – e2 = 1 – e3-1

 

Therefore,

1 – e3 = 1 – e4-1

1 – e4 = 1 – e5-1

 

Hence, the numerator of the nth term will be represented by 1 – en-1.

 

Consider the denominators of the terms. The denominator of the nth term will be represented by 1 + en.

 

Therefore, the explicit formula for the nth term of the sequence will be an = (1 – en-1)/(1 + en).

Therefore, the explicit formula for the nth term of the sequence will be an = (1 – en-1)/(1 + en).