Question

Find the missing terms of the arithmetic sequence..., 27, ?,?, ?, 53, .... Show each step of the process clearly.

Answer 1

Let the five consecutive terms be t1, t2, t3, t4, t5 with t1 = 27 and t5 = 53. For an arithmetic sequence each consecutive difference is the same, call it d.

1. There are 4 equal steps from t1 to t5, so
t5 = t1 + 4d → 53 = 27 + 4d.

2. Solve for d:
4d = 53 − 27 = 26 → d = 26/4 = 13/2 = 6.5.

3. Find the missing terms:
t2 = t1 + d = 27 + 6.5 = 33.5 (or 67/2),
t3 = t2 + d = 33.5 + 6.5 = 40,
t4 = t3 + d = 40 + 6.5 = 46.5 (or 93/2).

Checks: t4 + d = 46.5 + 6.5 = 53, so the sequence is correct.

Answer: 33.5, 40, 46.5.