given ,a=5,d=3,an=50,find n and sn

1.	given ,a=5,d=3,an=50,find n and sn
Answer» Here, a = 5, d = 3, an = 50We know thatan = a + (n – 1)d{tex} \\Rightarrow {/tex}50 = 5 + (n - 1)3{tex} \\Rightarrow {/tex} (n – 1)3 = 50 - 5{tex} \\Rightarrow {/tex}\xa0(n - 1)3 = 45{tex} \\Rightarrow n - 1 = \\frac{{45}}{3}{/tex}{tex} \\Rightarrow {/tex}\xa0n - 1 = 15{tex} \\Rightarrow {/tex}n = 15 + 1{tex} \\Rightarrow {/tex}n = 16Again, we know that{tex}{S_n} = \\frac{n}{2}\\left[ {2a + (n - 1)d} \\right]{/tex}{tex} \\Rightarrow {S_n} = \\frac{{16}}{2}\\left[ {2(5) + (16 - 1)3} \\right]{/tex}{tex} \\Rightarrow {/tex}\xa0Sn = 8[10 +45]{tex} \\Rightarrow {/tex}\xa0Sn = 8(55){tex} \\Rightarrow {/tex}\xa0Sn = 440

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