given ,a=5,d=3,an=50,find n and sn
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Sia ? 6 years, 4 months ago
Here, a = 5, d = 3, an = 50
We know that
an = a + (n – 1)d
{tex} \Rightarrow {/tex}50 = 5 + (n - 1)3
{tex} \Rightarrow {/tex} (n – 1)3 = 50 - 5
{tex} \Rightarrow {/tex} (n - 1)3 = 45
{tex} \Rightarrow n - 1 = \frac{{45}}{3}{/tex}
{tex} \Rightarrow {/tex} n - 1 = 15
{tex} \Rightarrow {/tex}n = 15 + 1
{tex} \Rightarrow {/tex}n = 16
Again, 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} Sn = 8[10 +45]
{tex} \Rightarrow {/tex} Sn = 8(55)
{tex} \Rightarrow {/tex} Sn = 440
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