An arithmetic sequence has a common difference of zero. The thirty-eighth term of the sequence is 2.1. What is the eighty-fifth term of the sequence?(1 point)
An arithmetic sequence with a common difference of zero means that all the terms in the sequence are the same. So, if the 38th term is 2.1, then every term after the 38th term will also be 2.1. Therefore, the 85th term of the sequence is also 2.1.
If an arithmetic sequence has a common difference of zero, it means that every term in the sequence is the same. In this case, since the thirty-eighth term is given as 2.1, we can conclude that all the terms in the sequence are 2.1.
Therefore, the eighty-fifth term of the sequence will also be 2.1.
Since the common difference is zero, each term of the sequence would be the same.
To find the value of the term in an arithmetic sequence, you can use the formula:
𝑎𝑛 = 𝑎₁ + (𝑛 − 1)𝑑
Where:
𝑎𝑛 = the 𝑛-th term
𝑎₁ = the first term
𝑑 = the common difference
𝑛 = the position of the term
In this case, since the common difference (𝑑) is zero, the formula simplifies to:
𝑎𝑛 = 𝑎₁
So, the 𝑛-th term is equal to the first term.
Given that the thirty-eighth term of the sequence is 2.1, we can conclude that the first term (𝑎₁) is also 2.1.
To find the eighty-fifth term (𝑎₈₅), we simply substitute the known values into the formula:
𝑎₈₅ = 𝑎₁ + (𝑛 − 1)𝑑
Since 𝑎₁ = 2.1, 𝑛 = 85, and 𝑑 = 0, we have:
𝑎₈₅ = 2.1 + (85 − 1) * 0
𝑎₈₅ = 2.1 + 84 * 0
𝑎₈₅ = 2.1 + 0
Therefore, the eighty-fifth term of the sequence is 2.1.
A recycling center began tracking the number of tires donated each day. At the end of the first day of their new tracking system, they counted 6 tires. At the end of the second day, 10 tires had been donated. At the end of the third day, 14 tires were collected. If you wrote an arithmetic sequence and a linear function that represented this scenario, what would be the difference between the initial value of the arithmetic sequence and the y-intercept of the linear function? (1 point)
The initial value of the arithmetic sequence and the y-intercept of the linear function are both 6 because it represents the number of tires collected on day 1.
The initial value of the arithmetic sequence is 6 because it represents the number of tires collected on day 1. The y-intercept of the linear function is 2 because that's the number of tires they had at the center before they started tracking their donations.
The initial value of the arithmetic sequence is 2 because that's the number of tires they had at the center before they started tracking their donations. The y-intercept of the linear function is 6 because it represents the number of tires collected on day 1.
The initial value of the arithmetic sequence and the y-intercept of the linear function are both 2 because that's the number of tires they had at the center before they started tracking their donations.
The correct answer is:
The initial value of the arithmetic sequence is 6 because it represents the number of tires collected on day 1. The y-intercept of the linear function is 6 because it also represents the number of tires collected on day 1.