Given the arithmetic sequence: $$ 14 ; 21 ; 28 ; \ldots, 336 $$. 1.1 How many terms are there in the sequence? 1.2 Calculate the sum of all the terms of the sequence.

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Let's analyze the given arithmetic sequence step by step.

**Given Sequence:** $$ 14 ; 21 ; 28 ; \ldots, 336 $$

- **First term (a₁):** 14
- **Common difference (d):** $$ 21 - 14 = 7 $$
- **Last term (aₙ):** 336

### 1.1. Number of Terms in the Sequence

To find the number of terms ($$ n $$) in an arithmetic sequence, use the formula for the $$ n $$-th term:
$$
a_n = a_1 + (n - 1)d
$$
Plugging in the known values:
$$
336 = 14 + (n - 1) \times 7
$$
$$
336 - 14 = (n - 1) \times 7
$$
$$
322 = (n - 1) \times 7
$$
$$
n - 1 = \frac{322}{7} = 46
$$
$$
n = 46 + 1 = 47
$$

**Answer:** There are **47 terms** in the sequence.

### 1.2. Sum of All Terms in the Sequence

The sum ($$ S_n $$) of the first $$ n $$ terms of an arithmetic sequence is given by:
$$
S_n = \frac{n}{2} \times (a_1 + a_n)
$$
Substituting the known values:
$$
S_{47} = \frac{47}{2} \times (14 + 336)
$$
$$
S_{47} = \frac{47}{2} \times 350
$$
$$
S_{47} = 47 \times 175 = 8,225
$$

**Answer:** The sum of all terms in the sequence is **8,225**.
There are 47 terms in the sequence, and the sum of all terms is 8,225.

Given the arithmetic sequence: .
1.1 How many terms are there in the sequence?
1.2 Calculate the sum of all the terms of the sequence.

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1.1. Number of Terms in the Sequence

1.2. Sum of All Terms in the Sequence

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Given the arithmetic sequence: . 1.1 How many terms are there in the sequence? 1.2 Calculate the sum of all the terms of the sequence.