The first term of a geometric sequence is -400, and the common ratio is −1/2.
What is the 10th term of the sequence?
To find the 10th term of the sequence, we can use the formula for the nth term of a geometric sequence:
T_n = a * r^(n-1)
where T_n is the nth term, a is the first term, r is the common ratio, and n is the position of the term we want to find.
In this case, a = -400, r = -1/2, and n = 10.
Plugging these values into the formula, we get:
T_10 = (-400) * (-1/2)^(10-1)
Simplifying:
T_10 = (-400) * (-1/2)^9
T_10 = (-400) * (-1/512)
T_10 = 400/512
T_10 = 25/32
So, the 10th term of the sequence is 25/32.
To find the 10th term of the sequence, we can use the formula for the nth term of a geometric sequence:
An = a * r^(n-1)
Where:
An = nth term
a = first term
r = common ratio
n = term number
Given:
a = -400
r = -1/2
n = 10
Substituting the values into the formula:
A10 = -400 * (-1/2)^(10-1)
A10 = -400 * (-1/2)^9
A10 = -400 * (-1/512)
A10 = 204800/512
A10 = 400
Therefore, the 10th term of the sequence is 400.
To find the 10th term of a geometric sequence, we can use the formula:
𝑎𝑛 = 𝑎₁ × 𝑟^(𝑛−1)
Where:
𝑎𝑛 is the nth term,
𝑎₁ is the first term, and
𝑟 is the common ratio.
In this case, the first term (𝑎₁) is -400, and the common ratio (𝑟) is -1/2. We want to find the 10th term (𝑎₁₀).
Substituting the values into the formula:
𝑎₁₀ = -400 × (-1/2)^(10-1)
Simplifying the exponent:
𝑎₁₀ = -400 × (-1/2)^9
Now, let's calculate (-1/2)^9:
(-1/2)^9 = -(1^9) / (2^9) = -1/512
Substituting back into the formula:
𝑎₁₀ = -400 × (-1/512)
To simplify this expression, we can cancel out 100 in the numerator and denominator:
𝑎₁₀ = -400 / (512/100) = -400 / 5.12
Calculating the division:
𝑎₁₀ ≈ 78.125
Therefore, the 10th term of the sequence is approximately 78.125.