Respuesta :
This is an arithmetic progression at a rate of 2/6.
So 1/6 + 2/6 = 3/6 (1/2)
3/6 + 2/6 = 5/6
5/6 + 2/6 = 7/6
....
29/6 + 2/6 = 31/6
31/6 +2/6 = 33/6 (11/2)
So 1/6 + 2/6 = 3/6 (1/2)
3/6 + 2/6 = 5/6
5/6 + 2/6 = 7/6
....
29/6 + 2/6 = 31/6
31/6 +2/6 = 33/6 (11/2)
Answer: The missing number in the sequence is [tex]\frac{7}{6}[/tex]
Step-by-step explanation:
Since we have given that
[tex]\frac{1}{6},\frac{1}{2},\frac{5}{6},----------,\frac{11}{2}[/tex]
First term = a= [tex]\frac{1}{6}[/tex]
Common difference = d is given by
[tex]d=a_2-a_1\\\\\frac{1}{2}-\frac{1}{6}\\\\=\frac{6-2}{12}\\\\=\frac{4}{12}=\frac{1}{3}\\\\Similarly,\\d=a_3-a_2\\\\=\frac{5}{6}-\frac{1}{2}\\\\=\frac{10-6}{12}\\\\=\frac{4}{12}\\\\=\frac{1}{3}[/tex]
Therefore, it forms an arithmetic sequence.
Since, [tex]a_4[/tex] is missing,
So,
[tex]a_4=a+3d\\\\a_4=\frac{1}{6}+3\times \frac{1}{3}\\\\a_4=\frac{1}{6}+1\\\\a_4=\frac{1+6}{6}\\\\a_4=\frac{7}{6}[/tex]
Hence, the missing number in the sequence is [tex]\frac{7}{6}[/tex]
