contestada

Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.)
{1, 1/3 , 1/5 , 1/7 , 1/9 , ...}
an = _________

Respuesta :

Answer:

[tex]a_n=\dfrac{1}{2n-1}[/tex]

Step-by-step explanation:

Given the sequence:

[tex]1, \frac{1}{3} , \frac{1}{5} , \frac{1}{7}, \frac{1}{9}, \cdots[/tex]

We observe that the numerator is always 1.

In the denominator, for each nth term, the multiple of 2 decreases by 1.

  • When n=1, Denominator =2(1)-1=1
  • When n=2, Denominator =2(2)-1=3
  • When n=3, Denominator =2(3)-1=5

We can, therefore, write the general term of the sequence as:

[tex]a_n=\dfrac{1}{2n-1}[/tex]