The first term of a geometric sequence is -400, and the common ratio is
−1/2
What is the 10th term of the sequence?
The formula for the nth term of a geometric sequence is given by:
\[a_n = a_1 \cdot r^{n-1}\]
where \(a_n\) is the nth term, \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the position of the term.
Given that the first term, \(a_1\), is -400 and the common ratio, \(r\), is -1/2, we can substitute these values into the formula to find the 10th term.
\[a_{10} = -400 \cdot \left(\frac{-1}{2}\right)^{10-1}\]
Simplifying the expression inside the brackets:
\[\left(\frac{-1}{2}\right)^{10-1} = \left(\frac{-1}{2}\right)^9 = \frac{1}{\left(\frac{1}{2}\right)^9} = 2^9 = 512\]
Substituting this value back into the formula:
\[a_{10} = -400 \cdot 512\]
Calculating the product, we get:
\[a_{10} = -204,800\]
Therefore, the 10th term of the sequence is -204,800.
To find the 10th term of a geometric sequence, we can use the formula:
𝑎𝑛 = 𝑎₁ * 𝑟^(𝑛−1)
where 𝑎₁ is the first term, 𝑟 is the common ratio, and 𝑛 is the position of the term.
Given that the first term, 𝑎₁, is -400 and the common ratio, 𝑟, is -1/2, we can substitute these values into the formula:
𝑎₁ = -400
𝑟 = -1/2
𝑛 = 10
𝑎₁₀ = -400 * (-1/2)^(10-1)
Simplifying this expression:
𝑎₁₀ = -400 * (-1/2)^9
To find the value of (-1/2)^9, we can convert this to a positive power by taking the reciprocal:
(-1/2)^9 = (1/(-1/2))^9 = (2/-1)^9 = -2^9 = -512
Substituting this value into the expression for 𝑎₁₀:
𝑎₁₀ = -400 * (-512)
Finally, we can calculate the value of 𝑎₁₀:
𝑎₁₀ = 204,800
Therefore, the 10th term of the sequence is 204,800.
To find the 10th term of the geometric sequence, we can use the formula for the nth term of a geometric sequence. The formula is:
an = a1 * r^(n-1)
where:
- an represents the nth term of the sequence
- a1 is the first term of the sequence
- r is the common ratio
- n is the position of the term we want to find
In this case, we are given:
- a1 = -400 (first term)
- r = -1/2 (common ratio)
- n = 10 (position of the term we want to find)
Substituting these values into the formula, we get:
a10 = (-400) * (-1/2)^(10-1)
Now we can simplify this expression to find the 10th term.