In an given AP,a=7,d13=35,find d1and s13

1.	In an given AP,a=7,d13=35,find d1and s13
Answer» Here, a = 7a13 = 35an\xa0= a + (n - 1)d{tex} \\Rightarrow {/tex}\xa0a13 = a + (13 - 1)d{tex} \\Rightarrow {/tex}\xa0a13 = a + 12d{tex} \\Rightarrow {/tex}\xa035 = 7 + 12d{tex} \\Rightarrow {/tex}\xa012d = 35 - 7{tex} \\Rightarrow {/tex}\xa012d = 28{tex} \\Rightarrow d = \\frac{{28}}{{12}}{/tex}{tex} \\Rightarrow d = \\frac{7}{3}{/tex}Again, we know that{tex}{S_n} = \\frac{n}{2}\\left[ {2a + (n - 1)d} \\right]{/tex}{tex} \\Rightarrow {S_{13}} = \\frac{{13}}{2}\\left[ {2a + (13 - 1)d} \\right]{/tex}{tex} \\Rightarrow {S_{13}} = \\frac{{13}}{2}\\left[ {2a + 12d} \\right]{/tex}{tex}={S_{13}} = \\frac{{13}}{2}\\left[ {2(7) + 12\\left( {\\frac{7}{3}} \\right)} \\right]{/tex}{tex} \\Rightarrow {S_{13}} = \\frac{{13}}{2}(14 + 28){/tex}{tex} \\Rightarrow {S_{13}} = \\frac{{13}}{2}(42){/tex}{tex} \\Rightarrow {S_{13}} = (13)(21){/tex}{tex} \\Rightarrow {S_{13}} = 273{/tex}

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