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In an application the sum of first n terms is 3n^2/2+13n/2.find it\'s 25 term. |
| Answer» According to the question,Given Sum of n terms {tex}\\left( {{S_n}} \\right) = \\frac{{3{n^2}}}{2} + \\frac{{13}}{2}n{/tex}Put n = 24, {tex}{S_{24}} = \\frac{{3 \\times 24 \\times 24}}{2} + \\frac{{13 \\times 24}}{2}{/tex}= 864 + 156= 1020Put n = 25, {tex}{S_{25}} = \\frac{{3 \\times 25 \\times 25}}{2} + \\frac{{13 \\times 25}}{2}{/tex}{tex} = \\frac{{1875}}{2} + \\frac{{325}}{2}{/tex}{tex} = \\frac{{2200}}{2} = 1100{/tex}{tex}\\therefore{/tex} 25th term (a{tex}_{25}{/tex}) = S25 - S24= 1100 - 1020= 80 | |