Find the sum of the first 25terms of an ap whose nth term is given by

1.	Find the sum of the first 25terms of an ap whose nth term is given by tn =7-3n
Answer» Given, {tex}n^{th}{/tex}\xa0term of an AP,\xa0{tex}{a_n} = 7-3n{/tex}{tex}\\therefore a= 7-3(1)=4{/tex}{tex}a_{25}=7-3(25)=-68{/tex}Sum of\xa0{tex}n{/tex}\xa0terms of an AP,{tex}S_n=\\frac{n}{2}(a+l){/tex}, where\xa0{tex}a {/tex}\xa0is the first term and\xa0{tex}l{/tex}\xa0is the last term ,here\xa0{tex}l=a_{25}{/tex}Clearly, sum of the first 25 terms, (S25){tex} = \\frac{{25}}{2}(a + {a_{25}}) {/tex}{tex}= \\frac{{25}}{2}[4 + (-68)]{/tex}{tex}= \\frac{25}{2}(-64){/tex}{tex}=25\\times(-32){/tex}{tex} = -800{/tex}

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