Know that the general rule for an arithmetic sequence is

,

where  represents the first number in the sequence,  is the common difference between consecutive numbers, and  is the -th number in the sequence.  

In our problem, .

Each time we move up from one number to the next, the sequence increases by 3.  Therefore, . 

The rule for this sequence is therefore .

The recursive formula for an arithmetic sequence is .

The only answer that fits this description is

.

This is an artithmetic series.  The explicit formula for an arithmetic sequence is:

Where represents the term, and is the common difference.

In this instance .  Therefore:

This is an arithmetic series. The formula to find the th term is:

where is the difference between each term.

To find the 35th term substitute for and

First, find a pattern in the sequence.  You will notice that each time you move from one number to the very next one, it increases by 7.  That is, the difference between one number and the next is 7.  Therefore, we can add 7 to 36 and the result will be 43.  Thus .

Determine what kind of sequence you have, i.e. whether the sequence changes by a constant difference or a constant ratio. You can test this by looking at pairs of numbers, but this sequence has a constant difference (arithmetic sequence).

So the sequence advances by subtracting 16 each time. Apply this to the last given term.

An arithmetic sequence adds or subtracts a fixed amount (the common difference) to get the next term in the sequence. If you know you have an arithmetic sequence, subtract the first term from the second term to find the common difference.

An arithmetic sequence adds or subtracts a fixed amount (the common difference) to get the next term in the sequence. If you know you have an arithmetic sequence, subtract the first term from the second term to find the common difference.

(i.e. the sequence advances by subtracting 27)

In each case, the terms increase by the same number, so all of these sequences are arithmetic.

Each term is the result of adding 1 to the previous term. 1 is the common difference.

Each term is the result of subtracting 1 from - or, equivalently, adding  to - the previous term.  is the common difference.

The common difference is 0 in a constant sequence such as this.

Each term is the result of adding  to the previous term.  is the common difference.

In an arithmetic sequence the amount that the sequence grows or shrinks by on each successive term is the common difference. This is a fixed number you can get by subtracting the first term from the second.

So the sequence is adding 12 each time. Add 12 to 25 to get the third term.

So the unknown term is 37. To double check add 12 again to 37 and it should equal the fourth term, 49, which it does.