Find the first term, a1, of an arithmetic sequence if a12 = 38 and a45 = 170.

-6

132/33

-5

6

Standard formula for arithmetic sequence:

an = a0 + d (n-1)

if we use the two terms given, setting a12 as starting term and a45 as the end term an.

170 = 38 + 33d

170 - 38 = 33d

132 = 33d

132/33 = d

This is the common difference, use it to find the first term.

38 = a0 + (132/33) (12-1)

38 = a0 + (132/33) (11)

38 = a0 + 132/3

38 - 132/3 = a0

38 - 44 = a0

-6 = a0

The starting term is - 6