Question

The 7th term and 10th term of an A.P are 12 and 25. Find the 12th term

Answer 1

`\: \huge \underline \pink{\mathbb{ANSWER}}`

Let assume a - first term and d - difference

`a _(7) = a_(1) + 6d = 12 \: \: \: \: \: \: ...(1)\\ \\ a_(10) = a_(1) + 9d = 25 \: \: \: \: ...(2) \\ \\ subtract \: \: eq(2) - eq(1) \\ \\ \: a + 9d - a + 6d = 25 - 12 \\ 3d = 13 \\ \\ d = (13)/(3) \\ \\ put \: value \: of \: \: d \: \: in \: eq(1) \\ \\ a_(1) + 6( (13)/(3) ) = 12 \\ \\ a_(1) + 26 = 12 \\ \\ a_(1) = - 14 \\ \\ for \: 12 {}^ {th} \: \: term \\ \\ a_(12) = a_(1) + d(n - 1) \\ \\ a_(12) = - 14 + (13)/(3) (12 - 1) \\ \\ a_(12) = - 14 + 47.66 \\ \\ a_(12) = \fbox{\green{ 33.66}}`