Multiple choice

If the 3rd term of the sequence is -9 and 8th term is 6, which term will be zero?

  1. 5

  2. 6

  3. 7

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In an arithmetic progression, a_n = a + (n-1)d. Given a_3 = a + 2d = -9 and a_8 = a + 7d = 6, subtracting these gives 5d = 15, so d = 3. Then a + 2(3) = -9, so a = -15. Setting a_n = -15 + (n-1)3 = 0 gives 3(n-1) = 15, so n-1 = 5, n = 6.

AI explanation

Assuming the sequence is an arithmetic progression, the common difference is calculated by dividing the difference between the eighth and third terms by the number of steps between them: (6 - (-9)) / (8 - 3) = 15 / 5 = 3. To reach zero from the third term (-9), we solve -9 + 3n = 0, where n is the number of steps needed; 3n = 9, so n = 3. Adding 3 steps to the third term gives the sixth term, meaning the sixth term is zero.

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