Question

The 3rd and 7th term of an arithmetic progression are -9 and 11 respectively. What is the 15th term?

Answer 1

$a3 = - 9 \\ a + 2d = - 9 \: \: \: \: \: \: \: \: \: \: \: \: (1)\\ a7 = 11 \\ a + 6d = 11 \: \: \: \: \: \: \: \: \: \: (2) \\ now \\ a + 2d = - 9 \\ a + 6d = 11 \\ ( - )( - ) \: ( - ) \\ - 4d = - 20 \\ \\ cancelling \: by \: - 4 \: we \: get \\ d = 5 \\ put \: d = 5 \: in \: eq \: 1 \\ a + 2(5) = - 9 \\ a + 10 = - 9 \\ a = - 9 - 10 \\ a = - 19$