Question

a sequence is defined by the following:
\\(a_1 = 6\\) and \\(a_n = -1.2 \cdot a_{n-1}\\)
what is the 4th term?
-12.4416
-10.368
10.368
12.4416

Explanation:

Identify the sequence type and parameters

Using the Geometric Sequences, Common Ratio, and Recursive Formulas knowledge points

$$
LATEXBLOCK0
$$

Calculate the second term

Using the Recursive Formulas knowledge point

$$ a_2 = -1.2 \cdot a_1 = -1.2 \cdot 6 = -7.2 $$

Calculate the third term

Using the Recursive Formulas knowledge point

$$ a_3 = -1.2 \cdot a_2 = -1.2 \cdot (-7.2) = 8.64 $$

Calculate the fourth term

Using the Recursive Formulas knowledge point

$$ a_4 = -1.2 \cdot a_3 = -1.2 \cdot 8.64 = -10.368 $$

Answer:

• (A) \(-12.4416\)
• (B) \(-10.368\) (Correct answer)
• (C) \(10.368\)
• (D) \(12.4416\)