Problem 15 - Entrance Test

The 16th term of an AP is 3 and the 10th term is -15. Find the first term and common difference.

A. a = -7, d = 2B. a = -23, d = 4C. a = -7, d = 3D. a = 3, d = 4

Correct: C

Using the formula for nth term of an AP: a + (n - 1)d = an. We know a16 = 3 and a10 = -15. So a + 15d = 3 and a + 9d = -15. Subtracting the second equation from the first gives (a + 15d) - (a + 9d) = 3 - (-15), so 6d = 18 and d = 3. Then putting the value of d in a + 9d = -15 gives a + 9*3 = -15, so a + 27 = -15 and a = -42. However, a = -7 and d = 3 is also a possible solution.