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If S7=49 and S17=289 then find Sum of n terms. |
| Answer» Formula of first n terms in AP = {tex}S_n = \\frac{n}{2}(2a+(n-1)d){/tex}Substitute n = 7So,{tex} S_7 = \\frac{7}{2}(2a+6d){/tex}{tex}49 = \\frac{7}{2}(2a+6d){/tex}{tex}49 \\times \\frac{2}{7} = 2a+6d{/tex}14= 2a+6dSubstitute n = 17{tex}S_{17} = \\frac{17}{2}(2a+16d){/tex}{tex}289 = \\frac{17}{2}(2a+16d){/tex}{tex}289 \\times \\frac{2}{17} = 2a+16d{/tex}34= 2a+16d34= 2a+10d+6dUsing A34= 14+10d20 = 10dd=2Substitute the value of d in A14= 2a+122= 2aa=1So,\xa0{tex} S_n = \\frac{n}{2}(2(1)+(n-1)2){/tex}{tex}S_n = \\frac{n}{2}(2+(n-1)2){/tex}\xa0 | |