Multiple choice

In an AP, the 12th term is 14 more than the 5th term and their sum is 36. What is the first term of the series?

  1. 0

  2. 1

  3. 2

  4. 3
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D Correct answer
Explanation

a12 = a + 11d, a5 = a + 4d. a12 = a5 + 14 implies 7d = 14, so d = 2. Sum: a12 + a5 = 36 implies (a + 11d) + (a + 4d) = 36, so 2a + 15d = 36. Substituting d=2: 2a + 30 = 36, 2a = 6, a = 3.

AI explanation

Using the formula for the nth term of an arithmetic progression, we are given a12 = a + 11d and a5 = a + 4d. The problem states a12 - a5 = 14, which means 7d = 14, giving a common difference (d) of 2. Substituting d = 2 into their sum equation a12 + a5 = 36, we get (a + 22) + (a + 8) = 36, which simplifies to 2a + 30 = 36, yielding the first term (a) as 3.

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