Question

Using the Formula for the General Term of an Arithmetic Sequence (to write a formula)

a) This is a question about solving a specific problem by writing a formula for the general term of an arithmetic sequence.
b) This is a question about the history of algebra.
c) This is a question about the properties of complex numbers.
d) This is a question about the development of mathematical logic.

Answer 1

the correct option is 'a)'. The question is about writing a formula for the general term of an arithmetic sequence, which is a mathematical problem typically encountered in high school.

Step-by-step explanation:

When tasked with writing a formula for the general term of an arithmetic sequence, we are dealing with a common problem in mathematics. An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant difference to the previous term. The formula we use to describe the n-th term of an arithmetic sequence is given by:

an = a1 + (n - 1)d

where an is the n-th term of the sequence, a1 is the first term, n is the term number, and d is the common difference between the terms.

For example, in the sequence 3, 5, 7, 9, ..., the first term a1 is 3 and the common difference d is 2. Therefore, the general term can be written as:

an = 3 + (n - 1)×2

Notably, the problem mentioned is not about the history of algebra, the properties of complex numbers, or the development of mathematical logic; hence the correct option is 'a)'.