a3 =15,s10=125, find d and a10

1.	a3 =15,s10=125, find d and a10
Answer» Here, a3 = 15S10 = 125We know thatan = a + (n - 1)d{tex} \\Rightarrow {/tex}\xa0a3 = a + (3 - 1)d{tex} \\Rightarrow {/tex}\xa0a3 = a + 2d{tex} \\Rightarrow {/tex}\xa015 = a + 2d{tex} \\Rightarrow {/tex}\xa0a + 2d = 15 ...... (1)Again, we know that{tex}{S_n} = \\frac{n}{2}\\left[ {2a + (n - 1)d} \\right]{/tex}{tex} \\Rightarrow {S_{10}} = \\frac{{10}}{2}\\left[ {2a + (10 - 1)d} \\right]{/tex}{tex} \\Rightarrow {/tex}\xa0S10 = 5(2a + 9d){tex} \\Rightarrow {/tex}\xa0125 = 5(2a + 9d){tex} \\Rightarrow {/tex}\xa025 = 2a + 9d{tex} \\Rightarrow {/tex}\xa02a + 9d = 25 ....... (2)Solving equation (1) and equation (2), we geta = 17d = -1Now an = a + (n - 1)d{tex} \\Rightarrow {/tex}\xa0a10 = a + (10 - 1)d{tex} \\Rightarrow {/tex}\xa0a10 = a + 9d{tex} \\Rightarrow {/tex}\xa0a10 = 17 + 9(-1){tex} \\Rightarrow {/tex}\xa0a10 = 17 - 9{tex} \\Rightarrow {/tex}\xa0a10 = 8

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