Question

The 10th term of an is -27 and the 5th term is -12.what is the 18th
term

Answer 1

$t_{10} = - 27\\ t_{5} \: = - 12 \\ \\ a + 9d = - 27 \\ a + 4d = - 12$

follow the attachment above ↗↗

$t_{18} = a + 17d \\ = 0 + 17 \times ( - 3) \\ = 0 - 51 \\ - 51$

Answer 2

Let a be the first term and d be the common difference
Then, given,
a10 = -27
a+9d =-27............(ii)
and also,
a5= -12
a+4d =-12 ..........(ii)
solving (i) & (ii), we get,
a = -24 & d = -3

therefore a18 = a+17d
= -24 + 17*-3
= -75