Third term of sequence a_n = (−1)^n (n-7) is :

Q: Third term of sequence a_n = (−1)^n (n-7) is :

To determine the third term of the sequence $ a_n = (-1)^n (n-7) $, we need to substitute $ n = 3 $ into the formula for the sequence. 1. **Calculate the third term:** \[ a_3 = (-1)^3 (3-7) \] \[ = (-1) \times (-4) \] \[ = 4 \] Therefore, the third term of the sequence is 4, which corresponds to Option 3. 2. **Explanation of why Option 3 is correct:** - The sequence is defined by the formula $ a_n = (-1)^n (n-7) $. For the third term, we substitute $ n = 3 $. - The calculation involves raising $-1$ to the power of 3, which results in $-1$, and then multiplying it by $(3-7)$, which is $-4$. - The product of $-1$ and $-4$ is $4$, confirming that the third term is indeed 4. 3. **Explanation of why other options are incorrect:** - **Option 1 (8):** This option is incorrect because the calculation results in 4, not 8. The sign and magnitude do not match the calculated value. - **Option 2 (-8):** This option is incorrect because the calculation results in a positive 4, not a negative 8. The sign is incorrect. - **Option 4 (-4):** This option is incorrect because the calculation results in a positive 4, not a negative 4. The sign is incorrect. By following the sequence formula and substituting the appropriate value for $ n $, we confirm that Option 3 is the correct answer.

Question

Accepted Answer

To determine the third term of the sequence $ a_n = (-1)^n (n-7) $, we need to substitute $ n = 3 $ into the formula for the sequence.

1. **Calculate the third term:**
   $$
   a_3 = (-1)^3 (3-7)
   $$
   $$
   = (-1) \times (-4)
   $$
   $$
   = 4
   $$

Therefore, the third term of the sequence is 4, which corresponds to Option 3.

2. **Explanation of why Option 3 is correct:**
   - The sequence is defined by the formula $ a_n = (-1)^n (n-7) $. For the third term, we substitute $ n = 3 $.
   - The calculation involves raising $-1$ to the power of 3, which results in $-1$, and then multiplying it by $(3-7)$, which is $-4$.
   - The product of $-1$ and $-4$ is $4$, confirming that the third term is indeed 4.

3. **Explanation of why other options are incorrect:**
   - **Option 1 (8):** This option is incorrect because the calculation results in 4, not 8. The sign and magnitude do not match the calculated value.
   - **Option 2 (-8):** This option is incorrect because the calculation results in a positive 4, not a negative 8. The sign is incorrect.
   - **Option 4 (-4):** This option is incorrect because the calculation results in a positive 4, not a negative 4. The sign is incorrect.

By following the sequence formula and substituting the appropriate value for $ n $, we confirm that Option 3 is the correct answer.