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

1.	Find the sum of the first 25 terms of an AP whose nth term is given by an=7-3n
Answer» Given, an\xa0= 7 - 3nPut\xa0n = 1, a1\xa0= 7\xa0- 3\xa0{tex}\\times{/tex}\xa01 = 7\xa0- 3 = 4Put\xa0n = 2, a2\xa0= 7\xa0- 3\xa0{tex}\\times{/tex}\xa02 = 7\xa0- 6 = 1Common difference(d) = 1 - 4\xa0=\xa0-3Sn\xa0=\xa0{tex}\\frac { n } { 2 } [ 2 a + ( n - 1 ) d ]{/tex}S25\xa0=\xa0{tex} \\frac { 25 } { 2 } [ 2 \\times 4 + ( 25 - 1 ) ( - 3 ) ]{/tex}{tex}= \\frac { 25 } { 2 } [ 8 - 72 ]{/tex}{tex}= \\frac { 25 } { 2 } \\times - 64{/tex}= -800

Discussion