Question

What is the General Term of an Arithmetic Sequence? (and its formula)

a) The general term of an arithmetic sequence is a formula used to find any term in the sequence. It is given by the formula: a_n = a_1 + (n - 1)d.
b) The general term of an arithmetic sequence is a formula used to find the sum of all terms in the sequence. It is given by the formula: S_n = n/2 (2a_1 + (n - 1)d).
c) The general term of an arithmetic sequence is a formula used to find the common difference between consecutive terms. It is given by the formula: d = (a_n - a_1) / (n - 1).
d) The general term of an arithmetic sequence is a formula used to find the initial term of the sequence. It is given by the formula: a_1 = a_n - (n - 1)d.

Answer 1

The general term of an arithmetic sequence is given by the formula a_n = a_1 + (n - 1)d, used to calculate any term in the sequence.

Step-by-step explanation:

The general term of an arithmetic sequence is used to find any specific term within the sequence, not the sum or the common difference. The formula for the general term is a_n = a_1 + (n - 1)d, where a_n is the nth term of the sequence, a_1 is the first term, n is the term number, and d is the common difference between consecutive terms.

This formula reflects the recursive nature of an arithmetic sequence by starting with the initial term and then adding the common difference repeatedly to reach subsequent terms. For instance, to find the 5th term in an arithmetic sequence where the first term is 2 and the common difference is 3, apply the formula to get a_5 = 2 + (5 - 1) × 3 = 14.