An arithmetic sequence has first term 8 and fourth term 14. What is its fifth term?

1. The common difference is added once to reach the second term, twice to reach the third and three times to reach the fourth. 2. So the fourth term equals the first term plus 3d, which gives 14 = 8 + 3d. 3. Subtracting 8 from both sides gives 3d = 6. 4. Dividing by 3 gives d = 2. 5. The fifth term is the fourth term plus one more common difference: 14 + 2 = 16. 6. Treating the fourth term as four steps from the first would give d = 1.5 and a fifth term of 15.5, so counting the steps is where this goes wrong. 7. Doubling 14 - 8 gives 12 and adding it to 8 gives 20, another way of mishandling the number of steps. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.2 Arithmetic Sequences_