Question

Identify the 42nd term of an arithmetic sequence where a1 = -12 and a27 = 66.

Answer 1

notice the common ratio between \(\bf \large a_1\quad and \quad a_27\)
there are 78 units between -12 and +66
and from the 1st term, to the 27th term, the common ratio has been used 26 times to get there

thus 78/26 will be the ratio

from there use the arithmetic sequence equation to find the 27th term \(\bf \large a_{27} = a_1+(27-1)\textit{common ratio}\)