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

Sum of the first 14 terms of an AP is 1505 and its first 10 term is 10

1.	Sum of the first 14 terms of an AP is 1505 and its first 10 term is 10.find its 25th term
Answer» Here a=10 and let d be the common difference. Then,S14=1505\xa0{tex}\\Rightarrow{/tex}\xa0{tex}\\frac{n}{2}{/tex}[2a+(n-1)d]=1505, where n=14 and a=10{tex}\\Rightarrow{/tex}\xa0{tex}\\frac{{14}}{2}{/tex}{tex} \\cdot {/tex}{tex}(20+13d)=1505\xa0{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}(20+13d)={/tex}{tex}\\frac{{1505}}{7}{/tex}{tex}=215{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}13d=195{/tex}\xa0{tex}\\Rightarrow{/tex}{tex}d=15.{/tex}Thus, a=10 and d=15.{tex}T_{25}\xa0= (a+24d)=(10+24\\times15)=370.{/tex}Hence, the 25th term is 370.