Arithmetic Sequence Question. Help!

Question

Given an arithmetic sequence which has a12=-2 and a16=-14 what is a23?

Answer 1

you have been given a₁₂ = -2 and a_{16 = -14.}

to get from the twelfth to the sixteenth element of an arithmetic sequence, the constant difference d would have been added 4 times, i.e. -2 + 4d = -14.

 

therefore 4d = -16; d = -4.

 

to get from a₁₆ to a₂₃ there will be 7 steps: a₂₃ = a₁₆ + 7d;

-14 + 7(-4) = -14 - 28 = -42