Question

find the first 20 term of an Ap whise 7 term is 24 less than the 11 term and first term begin with 12​

Answer 1

$\bf \underline{Answer : - } \\ \\ \sf \star \: let \: \: the \: \: first \: \: term \: \: (a) \: \: = 12 \\ \\ \sf \star \: common \: \: difference \: \: = d \\ \\ \sf \: n ^{th }\: \: term : - \\ \\ \sf \: a_n = a + (n - 1)d..........(1) \\ \\ \sf \: {7}^{th} \: \: term \: \: : - \\ \\ \sf \: a_7 = a + 6d............(2) \\ \\ \sf \: {11}^{th} \: \: term \: : - \\ \\ \sf \: a_{11} = a + 10d............(3) \\ \\ \bf \: given : \\ \\ \sf \: a_{11} - a_7 = 24 \\ \\ \sf \: a + 10d - (a + 6d) = 24 \\ \\ \sf \: a + 10d - a - 6d = 24 \\ \\ \sf \: 4d = 24 \\ \\ \sf \: d = 6 \\ \\ now \\ \\ \sf \: a_{20} = a + 19d \\ \\ \sf \: a_{20} = 12 + 19 \times 6 \\ \\ \sf \: a_{20} = 12 + 114 \\ \\ \sf \: a_{20} = 126$

20 th term of AP is 126!!!