Which expression gives the number in the nth position in the sequence?

To find the number in the nth position of a given sequence, we need to identify the pattern or formula that defines that sequence. For example, if we have a simple arithmetic sequence where each term increases by a fixed amount, the expression can often be defined as:

Expression: a_n = a_1 + (n - 1) * d

Where:

• a_n is the nth term of the sequence.
• a_1 is the first term in the sequence.
• d is the common difference between consecutive terms.
• n is the position of the term you want to find.

For different types of sequences, such as geometric or quadratic, the expressions will vary. For example, a geometric sequence where each term is multiplied by a fixed factor can be expressed as:

Expression: a_n = a_1 * r^(n-1)

Where r is the common ratio. Identifying the type of sequence is crucial in determining the correct expression to find the nth term.