Khalid wrote the sequence below. x - 1, -2x + 2, 4x - 4, -8x + 8. Which formula can be used to find the 10th term of the sequence?
a₁₀ = (x - 1)*(-2)^10-1
a₁₀ = (x - 1)^10-1
a₁₀ = (x - 1)*(2)^10-1
a₁₀ = (x - 1)*(-2)¹⁰

Solution:

Given, the sequence is x - 1, -2x + 2, 4x - 4, -8x + 8.

Common ratio, r = (-2x + 2) / (x - 1)

r = -2(x - 1) / (x - 1)

r = -2

Again, r = (4x - 4) / (-2x + 2)

r = 4(x - 1) / -2(x - 1)

r = -2

Therefore, the given series is in geometric progression.

We have to find the 10th term of the sequence.

The n-th term of a geometric sequence is given by a_n = ar^n-1

Here, a = x - 1, r = -2, n = 10.

a₁₀ = (x - 1)(-2)^10-1

a₁₀ = (x - 1)(-2)9 

a₁₀ = (x - 1)(256)

a₁₀ = 256x - 256

Therefore, the 10th term of the sequence is a₁₀ = (x - 1)(-2)^10-1 or 256x - 256.

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Khalid wrote the sequence below. x - 1, -2x + 2, 4x - 4, -8x + 8. Which formula can be used to find the 10th term of the sequence?

Summary:

Khalid wrote the sequence x - 1, -2x + 2, 4x - 4, -8x + 8. The 10th term of the sequence is a₁₀ = (x - 1)(-2)^10-1 or 256x - 256.