\begin{tabular}{|ll|}\hline QUESTION 4 \ Consider the linear pattern: $$ 5 ; 7 ; 9 ; \ldots $$ \ 4.1 & Determine $$ \mathrm{T}_{51} $$. \ 4.2 & Calculate the sum of the first 51 terms. \end{tabular}

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**Problem 4:**

Consider the arithmetic sequence: $$ 5, \; 7, \; 9, \; \ldots $$

- **First term ($$ T_1 $$)**: 5
- **Common difference ($$ d $$)**: $$ 7 - 5 = 2 $$

---

### 4.1 Determine $$ T_{51} $$

The general formula for the $$ n $$-th term of an arithmetic sequence is:

$$
T_n = T_1 + (n - 1) \times d
$$

Plugging in the values:

$$
T_{51} = 5 + (51 - 1) \times 2 = 5 + 50 \times 2 = 5 + 100 = 105
$$

**Answer:** $$ T_{51} = 105 $$

---

### 4.2 Calculate the sum of the first 51 terms

The formula for the sum of the first $$ n $$ terms ($$ S_n $$) of an arithmetic sequence is:

$$
S_n = \frac{n}{2} \times (T_1 + T_n)
$$

First, we already determined $$ T_{51} = 105 $$. Now, plug in the values:

$$
S_{51} = \frac{51}{2} \times (5 + 105) = \frac{51}{2} \times 110 = 51 \times 55 = 2805
$$

**Answer:** The sum of the first 51 terms is **2805**.
**Problem 4:** Consider the arithmetic sequence: $$ 5, \; 7, \; 9, \; \ldots $$ - **First term ($$ T_1 $$)**: 5 - **Common difference ($$ d $$)**: 2 --- ### 4.1 Determine $$ T_{51} $$ $$ T_{51} = 5 + (51 - 1) \times 2 = 5 + 100 = 105 $$ **Answer:** $$ T_{51} = 105 $$ --- ### 4.2 Calculate the sum of the first 51 terms $$ S_{51} = \frac{51}{2} \times (5 + 105) = 51 \times 55 = 2805 $$ **Answer:** The sum of the first 51 terms is **2805**.

QUESTION 4

Consider the linear pattern:

4.1 Determine .

4.2 Calculate the sum of the first 51 terms.

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4.1 Determine

4.2 Calculate the sum of the first 51 terms

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QUESTION 4
Consider the linear pattern:
4.1	Determine .
4.2	Calculate the sum of the first 51 terms.

QUESTION 4 Consider the linear pattern: 4.1 Determine . 4.2 Calculate the sum of the first 51 terms.