Question

khalid wrote the sequence below

\\(x - 1, -2x + 2, 4x - 4, -8x + 8, \dots\\)

which formula can be used to find the 10th term of the sequence?

\\(a_{10} = (x - 1)(-2)^{10-1}\\)

\\(a_{10} = (x - 1)^{10-1}\\)

\\(a_{10} = (x - 1)(2)^{10-1}\\)

\\(a_{10} = (x - 1)(-2)^{10}\\)

Explanation:

Identify the first term of the sequence

Using the Geometric Sequences knowledge point

$$ a_1 = x - 1 $$

Determine the common ratio

Using the Common Ratio knowledge point

$$ r = \frac{a_2}{a_1} = \frac{-2x + 2}{x - 1} = \frac{-2(x - 1)}{x - 1} = -2 $$

Apply the explicit formula for the 10th term

Using the Geometric Sequence Explicit Formula knowledge point

$$ a_n = a_1 \cdot r^{n-1} \implies a_{10} = (x - 1)(-2)^{10-1} $$

Answer:

• (A) \(a_{10} = (x - 1)(-2)^{10-1}\) (Correct answer)
• (B) \(a_{10} = (x - 1)^{10-1}\)
• (C) \(a_{10} = (x - 1)(2)^{10-1}\)
• (D) \(a_{10} = (x - 1)(-2)^{10}\)