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IN AN AP. GIVEN d=5,s9=75 find a and a9 |
| Answer» Here, d = 5S9 = 75We know that{tex}{S_n} = \\frac{n}{2}\\left[ {2a + (n - 1)d} \\right]{/tex}{tex} \\Rightarrow {S_9} = \\frac{9}{2}\\left[ {2a + (9 - 1)d} \\right]{/tex}{tex} \\Rightarrow {S_9} = \\frac{9}{2}\\left[ {2a + 8d} \\right]{/tex}{tex} \\Rightarrow {S_9} = 9\\left[ {a + 4d} \\right]{/tex}{tex} \\Rightarrow {S_9} = 9\\left[ {a + 4 \\times 5} \\right]{/tex}{tex} \\Rightarrow {/tex}\xa0S9 = 9[a + 20]{tex} \\Rightarrow {/tex}\xa075 = 9a + 180{tex} \\Rightarrow {/tex}\xa09a = 75 - 180{tex} \\Rightarrow {/tex}\xa09a = -105{tex} \\Rightarrow a = - \\frac{{105}}{9}{/tex}{tex} \\Rightarrow a = - \\frac{{35}}{3}{/tex}Again, we know thatan = a + (n - 1)d{tex} \\Rightarrow {/tex}\xa0a9 = a + (9 - 1)d{tex} \\Rightarrow {/tex}\xa0a9 = a + 8d{tex} \\Rightarrow {a_9} = - \\frac{{35}}{3} + 8(5){/tex}{tex} \\Rightarrow {a_9} = - \\frac{{35}}{3} + 40{/tex}{tex} \\Rightarrow {a_9} = \\frac{{ - 35 + 120}}{3}{/tex}{tex} \\Rightarrow {a_9} = \\frac{{85}}{3}{/tex} | |