The explicit formula is tn = -1/3 + 2/3(n - 1) and the value of t20 is 37/3
How to determine the explicit formula?
The terms of the sequence are given as:
t2 = 1/3
t8 = 13/3
An arithmetic sequence is represented as:
tn = a + (n - 1)d
So, we have:
t2 = a + d
t8 = a + 7d
This implies that
a + d = 1/3
a + 7d = 13/3
Subtract the equations
6d = 12/3
Solve for d
d = 2/3
Substitute d = 2/3 in a + d = 1/3
a + 2/3 = 1/3
Solve for a
a = -1/3
Substitute d = 2/3 and a = -1/3 in tn = a + (n - 1)d
tn = -1/3 + 2/3(n - 1)
Hence, the explicit formula is tn = -1/3 + 2/3(n - 1)
The value of t20
This means that n = 20.
So, we have:
t20 = -1/3 + 2/3(20 - 1)
Evaluate
t20 = 37/3
Hence, the value of t20 is 37/3
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