Question

The sum of the 4th and 8th terms of an AP is 24,then it's 6th term is *

Answer 1

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$let \: a \: be \: the \: first \: term \: and \: d \: be \: the \: common \: difference \: of \: the \: ap \\ then \\ t _{4} + t _{8} = 24 \implies(a + 3d) + (a + 7d) = 24 \\ \implies2a + 10d = 24 \\ \implies \: a + 5d = 12 \: \: \: \: .......(1) \\ and \: t _{6} + t _{10} \implies(a + 5d) + (a + 9d) = 44 \\ \implies2a + 14d = 44 \\ \implies \: a + 7d = 22 ........(2)\\ on \: solving \: (1)and(2) \: we \: get \: a = - 13 \: and \: d= 5 \\ \therefore \: first \: three \: terms \: are \: - 13 \:, - 8 \: and \: - 3$