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.

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**.