Understanding the Arithmetic Sequence

The question asks us to find the 20th term of the sequence: -50, -47, -44, ...

First, let's determine the type of sequence. We check the difference between consecutive terms:

• The difference between the second term (-47) and the first term (-50) is: $$-47 - (-50) = -47 + 50 = 3$$
• The difference between the third term (-44) and the second term (-47) is: $$-44 - (-47) = -44 + 47 = 3$$

Since the difference between consecutive terms is constant (3), this is an arithmetic sequence.

Identifying Key Parameters

For an arithmetic sequence, we need to know:

• The first term ($a_1$): In this sequence, the first term is -50.
• The common difference ($d$): We calculated the common difference to be 3.
• The term number ($n$) we need to find: We are looking for the 20th term, so $n = 20$.

Formula for the nth Term

The formula to find the $n$-th term ($a_n$) of an arithmetic sequence is:

$$a_n = a_1 + (n-1)d$$

Where:

• $a_n$ is the $n$-th term
• $a_1$ is the first term
• $n$ is the term number
• $d$ is the common difference

Calculating the 20th Term

Now, we substitute the values we identified into the formula:

• $a_1 = -50$
• $n = 20$
• $d = 3$

Plugging these into the formula:

$$a_{20} = -50 + (20-1) \times 3$$

First, calculate the value inside the parenthesis:

$$a_{20} = -50 + (19) \times 3$$

Next, perform the multiplication:

$$a_{20} = -50 + 57$$

Finally, perform the addition:

$$a_{20} = 7$$

Conclusion

Therefore, the 20th term in the given arithmetic sequence is 7.