Multiple choice

If the $14^{th}$ term of an arithmetic series is $6$ and $6^{th}$ term is $14$, then what is the $95^{th}$ term?

  1. $-75$
  2. $75$
  3. $80$
  4. $-80$
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A Correct answer
Explanation

a + 13d = 6, a + 5d = 14. Subtracting: 8d = -8 => d = -1. a + 5(-1) = 14 => a = 19. 95th term = a + 94d = 19 + 94(-1) = 19 - 94 = -75.

AI explanation

Using the arithmetic progression formula a_n = a + (n-1)d, we set up two equations based on the given terms: a + 13d = 6 and a + 5d = 14. Subtracting the second equation from the first yields 8d = -8, so the common difference d is -1. Substituting d = -1 into the second equation gives a first term a of 19. To find the 95th term, calculate 19 + (95-1)(-1), which simplifies to 19 - 94, resulting in -75.

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