Multiple choice

If 6th and 7th terms of an AP are the larger and smaller roots of the equation x2 - 15x + 56 = 0 respectively, then 2020th term is

  1. -2004

  2. -2006

  3. -2000

  4. 2005

  5. -1996
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B Correct answer
Explanation

Roots of x^2 - 15x + 56 = 0 are 7 and 8. 6th term = 8, 7th term = 7. Common difference d = 7 - 8 = -1. First term a = 8 - 5(-1) = 13. 2020th term = a + 2019d = 13 + 2019(-1) = 13 - 2019 = -2006.

AI explanation

Factoring the quadratic equation x^2 - 15x + 56 = 0 gives (x - 8)(x - 7) = 0, meaning the larger root is 8 and the smaller root is 7. The 6th term is 8 and the 7th term is 7, so the common difference of the arithmetic progression is -1, making the first term a = 8 - 5(-1) = 13. Using the arithmetic progression formula for the nth term, the 2020th term is 13 + (2020 - 1)(-1), which equals 13 - 2019, resulting in -2006.

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