Answer :
The n-th term of the Arithmetic sequence is 1/7( 2 + n) and the tenth term [tex]a_{10}[/tex] = 12/7
What is arithmetic progression?
Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.
In the given sequence, the first term a = 3/7
second term (a + d) = 4/7
common difference(d) = 4/7 - 3/7
d = 1/7
The nth term of an Arithmetic sequence [tex]a_{n}[/tex] = a + ( n -1) d
substitute a and d into the equation above
[tex]a_{n}[/tex] = 3/7 + (n - 1) x 1/7
simplifying and factoring out 1/7
we have
1/7( 3 + n - 1)
= 1/7( 2 + n)
The tenth term [tex]a_{10}[/tex] = 1/7( 2 + 10)
[tex]a_{10}[/tex] = 12/7
In conclusion, the nth term of the sequence is 1/7( 2 + n) and the tenth term is 12/7
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