Step-by-step explanation:
Since the sequence above is an arithmetic sequence
For an nth term in an arithmetic sequence
A(n) = a + ( n - 1)d
where a is the first term
n is the number of terms
d is the common difference
From the question
a = 1/3
d = 1/2 - 1/3 = 1/6 or 2/3 - 1/2 = 1/6
Substitute the values into the above formula
That's
[tex]A(n) = \frac{1}{3} + (n - 1) \frac{1}{6} \\ = \frac{1}{ 3} - \frac{1}{6} + \frac{1}{6} n [/tex]
So the nth term of the sequence is
[tex]A(n) = \frac{1}{6} + \frac{1}{6}n[/tex]
For a50 since we are finding the 50th term
n = 50
So we have
[tex]A(50) = \frac{1}{6} + \frac{1}{6} (50) \\ = \frac{1}{6} + \frac{25}{3} [/tex]
We have the final answer as
[tex]A(50) = \frac{17}{2} [/tex]
Hope this helps you
