To solve for the first term $a_1$ and the number of terms $n$ in the arithmetic sequence, we will use the following information:

• The sum of the first $n$ terms of the arithmetic sequence is given as $S_n = 438$.
• The last term $a_n = 35$.
• The common difference $d = 7$.

We have the formulas for an arithmetic sequence:

1. Sum of the first $n$ terms: $S_n = \frac{n}{2} \times (a_1 + a_n)$
2. $n$-th term of an arithmetic sequence: $a_n = a_1 + (n - 1) \cdot d$

Step 1: Use the sum formula

We substitute $S_n = 438$, $a_n = 35$, and the formula for the sum: $438 = \frac{n}{2} \times (a_1 + 35)$ Simplifying: $438 = \frac{n}{2} \times (a_1 + 35) \implies 876 = n \times (a_1 + 35)$ $n(a_1 + 35) = 876 \quad \text{(Equation 1)}$

Step 2: Use the formula for the $n$-th term

We know that the last term $a_n = 35$, so using the formula for the $n$-th term: $35 = a_1 + (n - 1) \cdot 7$ Simplifying: [ 35 = a_1 + 7n - 7