if the first and last terms of an ap is 5 and 45 and sum of its terms is 400,then the number of terms of an ap is
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if the first and last terms of an ap is 5 and 45 and sum of its terms is 400,then the number of terms of an ap is
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Answer:-
We know that
[tex]\boxed{\sf S_n=\dfrac{n}{2}(a+\ell)}[/tex]
[tex]\\ \sf{:}\longrightarrow 400=\dfrac{n}{2}(5+45)[/tex]
[tex]\\ \sf{:}\longrightarrow 400=\dfrac{n}{2}(50)[/tex]
[tex]\\ \sf{:}\longrightarrow 400=\dfrac{50n}{2}[/tex]
[tex]\\ \sf{:}\longrightarrow 50n=400(2)[/tex]
[tex]\\ \sf{:}\longrightarrow 50n=800[/tex]
[tex]\\ \sf{:}\longrightarrow n=\dfrac{800}{50}[/tex]
[tex]\\ \sf{:}\longrightarrow n=16[/tex]
Hence number of terms =16.