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Sia ? 6 years, 5 months ago
The given AP is {tex} - 3,\frac{1}{2},2,......{/tex}
Here, a = -3
{tex}d = - \frac{1}{2} - ( - 3) = - \frac{1}{2} + 3 = \frac{5}{2}{/tex}
and n = 11
a11 = ?
We have, an = a + (n - 1)d
So, {tex}{a_{11}} = - 3 + (11 - 1)\left( {\frac{5}{2}} \right){/tex}
{tex} \Rightarrow {a_{11}} = - 3 + 25{/tex}
{tex} \Rightarrow {a_{11}} = 22{/tex}
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Sia ? 6 years, 5 months ago
According to the question,we have,
a=9. Therefore, common difference d =17-9=8
let the required number of terms be n.
Therefore, Sn=636
{tex}\Rightarrow{/tex}{tex}\frac{n}{2}{/tex}[2a+(n-1)d]=636
{tex}\Rightarrow{/tex}{tex}\frac{n}{2}{/tex}[2(9)+(n-1)8]=636
{tex}\Rightarrow{/tex}n[18+8n-8]=1272
{tex}\Rightarrow{/tex}8n2+10n-1272=0
{tex}\Rightarrow{/tex}4n2+5n-636=0
{tex}\Rightarrow{/tex}4n2+53n-48n-636=0
{tex}\Rightarrow{/tex}n(4n+53)-12(4n+53)=0
{tex}\Rightarrow{/tex}(4n+53)(n-12)=0
{tex}\Rightarrow{/tex}4n+53=0 or n-12=0
{tex}\Rightarrow{/tex}n={tex}\frac{{ - 53}}{4}{/tex} or n=12
Since number of terms cannot neither be negative nor fraction, n=12
hence, the required number of terms is 12.
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Surendrapal Singh Singh Gaur 7 years, 4 months ago
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