To find the 75th term of an arithmetic sequence, we need to identify the first term and the common difference.

The arithmetic sequence is: $-1, 15, 31, \dots$

Step 1: Identify the First Term ($a$) and the Common Difference ($d$)

• The first term $a = -1$.
• The common difference $d$ can be calculated by subtracting the first term from the second term: $d = 15 - (-1) = 15 + 1 = 16$

Step 2: Use the Formula for the $n$th Term of an Arithmetic Sequence

The $n$th term of an arithmetic sequence is given by: $a_n = a + (n - 1) \cdot d$

We need the 75th term, so let $n = 75$: $a_{75} = -1 + (75 - 1) \cdot 16$ $a_{75} = -1 + 74 \cdot 16$ $a_{75} = -1 + 1184$ $a_{75} = 1183$

Answer

The 75th term of the sequence is 1183.

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Here are some related questions for further practice:

1. How do you find the sum of the first 75 terms in this sequence?
2. What is the general formula for any term in this arithmetic sequence?
3. How can we determine if a number is part of this arithmetic sequence?
4. How would you find the common difference if only given non-consecutive terms?
5. What is the 100th term of this sequence?

Tip: In an arithmetic sequence, once you know the first term and the common difference, you can calculate any term directly!