The nth term of a sequence is n2 - 6n - 4. Find the sum of the 3rd and 4th terms.

1. Analyze the question

We are given a formula for the $n^{th}$ term of a sequence: $T_n = n^2 - 6n - 4$. We need to find the sum of the 3rd term ($T_3$) and the 4th term ($T_4$).

2. Explain the concept

To find any specific term in a sequence when given the general formula, we simply substitute the value of $n$ (the position of the term) into the expression. Once we calculate $T_3$ and $T_4$ individually, we add them together to get the final result.

3. Show the solution

Step 1: Find the 3rd term ($T_3$) Substitute $n = 3$ into the formula $n^2 - 6n - 4$: $T_3 = (3)^2 - 6(3) - 4$ $T_3 = 9 - 18 - 4$ $T_3 = -9 - 4$ $T_3 = -13$

Step 2: Find the 4th term ($T_4$) Substitute $n = 4$ into the formula $n^2 - 6n - 4$: $T_4 = (4)^2 - 6(4) - 4$ $T_4 = 16 - 24 - 4$ $T_4 = -8 - 4$ $T_4 = -12$

Step 3: Find the sum of the 3rd and 4th terms Sum $= T_3 + T_4$ Sum $= (-13) + (-12)$ Sum $= -25$

4. Identify the answer

Comparing our result to the given options: A. 24 B. 23 C. -24 D. -25

The correct option is D.

5. Tip

When dealing with sequences involving negative numbers, always be careful with your signs during subtraction. A common mistake is to calculate $9 - 18$ as $9$ instead of $-9$. Always perform the operations from left to right to stay organized!