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.

To find the number of terms in the arithmetic sequence \( 14, 21, 28, \ldots, 336 \), we can use the formula for the \( n \)-th term of an arithmetic sequence: \[ a_n = a_1 + (n-1)d \] where \( a_1 \) is the first term, \( d \) is the common difference, and \( a_n \) is the \( n \)-th term. Here, \( a_1 = 14 \) and \( d = 21 - 14 = 7 \). We set \( a_n = 336 \) to find \( n \): \[ 336 = 14 + (n-1) \cdot 7 \] \[ 336 - 14 = (n - 1) \cdot 7 \] \[ 322 = (n - 1) \cdot 7 \] \[ n - 1 = \frac{322}{7} = 46 \] \[ n = 47 \] So, there are \( 47 \) terms in the sequence. Next, to calculate the sum of all the terms in the sequence, we can use the sum formula for an arithmetic series: \[ S_n = \frac{n}{2} (a_1 + a_n) \] Substituting \( n = 47 \), \( a_1 = 14 \), and \( a_n = 336 \): \[ S_{47} = \frac{47}{2} (14 + 336) \] \[ = \frac{47}{2} \cdot 350 \] \[ = 47 \cdot 175 \] \[ = 8225 \] Thus, the sum of all the terms in the sequence is \( 8225 \).