Answer:
10
Step-by-step explanation:
Let $a_n$ be the $n$th term of this sequence. We know $a_2 + a_8 = 5$, and that forces $a_5 = \dfrac 5 2$, the average of these terms.
Then $a_4a_5 = 5$ gives us $a_4 = 2$.
The common difference is $\dfrac 1 2$, and in general, $a_n = \dfrac n 2$.
Therefore the $20$th term is $\dfrac{20}{2} = \boxed{10}$.
The 20th term of the arithmetic sequence will be equal to [tex]T_{20}=10[/tex]
Arthematic sequence is the type of the number series in which the difference between the first and the second term is always constant in the whole series.
Let [tex]$a_n$[/tex] be the nth term of this sequence.
We know
[tex]$a_2 + a_8 = 5$[/tex], and that forces [tex]$a_5 = \dfrac 5 2$[/tex], the average of these terms.
Then [tex]$a_4a_5 = 5$[/tex] gives us [tex]a_4 = 2$.[/tex]
The common difference is [tex]\dfrac 1 2$,[/tex]and in general, [tex]$a_n = \dfrac n 2$[/tex].
Therefore the 20th term is
[tex]T_{20}=$\dfrac{20}{2} = \boxed{10}$.[/tex]
Hence the 20th term of the arithmetic sequence will be equal to [tex]T_{20}=10[/tex]
To know more about arthematic sequence follow
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