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Sum of the first 14 terms of an AP is 1505 and its first 10 term is 10.find its 25th term

Posted by Biplab Sarkar 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Here a=10 and let d be the common difference. Then,
S₁₄=1505 {tex}\Rightarrow{/tex} {tex}\frac{n}{2}{/tex}[2a+(n-1)d]=1505, where n=14 and a=10
{tex}\Rightarrow{/tex} {tex}\frac{{14}}{2}{/tex}{tex} \cdot {/tex}{tex}(20+13d)=1505 {/tex}
{tex}\Rightarrow{/tex} {tex}(20+13d)={/tex}{tex}\frac{{1505}}{7}{/tex}{tex}=215{/tex}
{tex}\Rightarrow{/tex} {tex}13d=195{/tex}

{tex}\Rightarrow{/tex}{tex}d=15.{/tex}
Thus, a=10 and d=15.
{tex}T_{25} = (a+24d)=(10+24\times15)=370.{/tex}
Hence, the 25th term is 370.

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