If 4m + 8, 2m² + 3m + 6, 3m² + 4m + 4 are three consecutive terms of an A.P. find m.

JAMB Mathematics 2024 312 views
Source: JAMB · 2024

If 4m + 8, 2m² + 3m + 6, 3m² + 4m + 4 are three consecutive terms of an A.P. find m.

  1. m = -1, 2
  2. m = -2, 0
  3. m = 0, 2 ✓
  4. m = 3, -2
Explanation

In an A.P., the middle term is the average of its neighbours, so 2 × (middle) = first + third.

2(2m² + 3m + 6) = (4m + 8) + (3m² + 4m + 4)

4m² + 6m + 12 = 3m² + 8m + 12, so m² − 2m = 0, which gives m(m − 2) = 0.

So m = 0 or 2.

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