Question

the seventh term of an arithmetic sequence is 10.2 and the twelfth term is 17.7.

what is the common difference of the arithmetic sequence?
the common difference is 1.5

use the explicit formula to find \\(a_1\\).
\\(a_1 = 1.2\\)

what is the explicit formula for the arithmetic sequence?
\\(a_n = 1.2 + (n - 1)1.5\\)
\\(a_n = 1.5 + (n - 1)1.2\\)
\\(a_n = 1.5 + (n - 1)3.9\\)
\\(a_n = 3.9 + (n - 1)1.5\\)

Explanation:

Identify the given sequence parameters

Using the Arithmetic Sequences and Sequence Notation knowledge points

$$
LATEXBLOCK0
$$

Write the explicit formula

Using the Arithmetic Sequences knowledge point

$$
LATEXBLOCK1
$$

Answer:

• (A) \(a_n = 1.2 + (n - 1)1.5\) (Correct answer)
• (B) \(a_n = 1.5 + (n - 1)1.2\)
• (C) \(a_n = 1.5 + (n - 1)3.9\)
• (D) \(a_n = 3.9 + (n - 1)1.5\)