To solve the problems in this image, let’s look at each arithmetic sequence individually.

Problem 1: Sequence - 35, 32, 29, 26, ...

1. Identify the first term (a₁): The first term, $a_1$, is 35.
2. Determine the common difference (d): Find the difference between consecutive terms.
   • $32 - 35 = -3$
   • Therefore, $d = -3$.
3. General formula for the nth term of an arithmetic sequence: $a_n = a_1 + (n - 1) \cdot d$
4. Substitute the values: $a_n = 35 + (n - 1) \cdot (-3)$ $a_n = 35 - 3(n - 1)$ $a_n = 38 - 3n$ This is the formula for the $n$-th term of the sequence.

Problem 2: Sequence - 10, 20, 30, 40, ...

1. Identify the first term (a₁): The first term, $a_1$, is 10.
2. Determine the common difference (d): Find the difference between consecutive terms.
   • $20 - 10 = 10$
   • Therefore, $d = 10$.
3. General formula for the nth term: $a_n = a_1 + (n - 1) \cdot d$
4. Substitute the values: $a_n = 10 + (n - 1) \cdot 10$ $a_n = 10 + 10n - 10$ $a_n = 10n$ This is the formula for the $n$-th term of the sequence.

Let me know if you would like a detailed explanation of these steps or if you have more questions.

Further Practice Questions:

1. What would be the 10th term of the first sequence (35, 32, 29, 26, …)?
2. What is the sum of the first 5 terms in the sequence 10, 20, 30, 40, …?
3. How would you find the common difference if only the first and fifth terms of an arithmetic sequence are known?
4. If the nth term of an arithmetic sequence is given as $a_n = 5n + 2$, what is the common difference?
5. What is the difference between an arithmetic sequence and a geometric sequence?

Tip:

In arithmetic sequences, each term changes by the same fixed amount, known as the common difference.