Question

In a geometric sequence, it is known that a₁ =-1 and a₄ = 64. The value of a₁₀ is

(1) -65.536
(2) 262,144
(3) 512
(4) -4096

Answer 1

To find the value of a₁₀ in the geometric sequence with a common ratio of -4, we can use the formula aₙ = a₁ * r^(n-1). Plugging in the given values, we find that a₁₀ is 262,144.

Step-by-step explanation:

To find the value of a₁₀ in the geometric sequence, we need to determine the common ratio (r). We can use the formula aₙ = a₁ * r^(n-1) where aₙ is the nth term of the sequence and n is the position of the term. We are given that a₁ = -1 and a₄ = 64. Plugging these values into the formula, we have:

1. a₄ = a₁ * r^(4-1)
2. 64 = -1 * r³
3. r³ = -64
4. r = -4

Now that we know the common ratio (r = -4), we can find a₁₀:

1. a₁₀ = a₁ * r^(10-1)
2. a₁₀ = -1 * (-4)⁹
3. a₁₀ = -262,144

Therefore, the value of a₁₀ is 262,144 (option 2).