In an ap the first term is 8 n term is 33 and sum of first n term is 1

1.	In an ap the first term is 8 n term is 33 and sum of first n term is 123 find n and d
Answer» Given First term (a) = 8and, nth term (an) = 33{tex}\\Rightarrow{/tex} a + (n - 1)d = 33{tex}\\Rightarrow{/tex} 8 + (n - 1)d = 33{tex}\\Rightarrow{/tex} (n - 1)d = 33 - 8{tex}\\Rightarrow{/tex} (n - 1)d = 25 .....(i)and, Sum of first n terms = 123{tex} \\Rightarrow \\frac{n}{2}\\left[ {a + {a_n}} \\right] = 123{/tex}{tex}\\Rightarrow \\frac{n}{2}\\left[ {8 + 33} \\right] = 123{/tex}{tex} \\Rightarrow \\frac{n}{2} \\times 41 = 123{/tex}{tex} \\Rightarrow n = \\frac{{123 \\times 2}}{{41}}{/tex}{tex}\\Rightarrow{/tex} n = 6Put value of n in equation (i)(6 - 1)d = 25{tex}\\Rightarrow{/tex} 5d = 25{tex}\\Rightarrow d = \\frac{{25}}{5} = 5{/tex}

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