Find the 10th term of a linear sequence whose 2nd term is 28 and 17th term is -2
d = (-2-28)/(17-2) = ___
a10 = a2+8d = ____
d=(-228)/(17-2)=
To find the 10th term of the linear sequence, we need to first determine the common difference (d) between consecutive terms.
We can calculate the common difference by subtracting the 2nd term (28) from the 17th term (-2) and then dividing by the number of terms between them:
d = (-2 - 28) / (17 - 2)
d = -30 / 15
d = -2
Now that we have the common difference (d = -2), we can use it to find the 10th term of the sequence.
To find the 10th term (a10), we can use the formula for the nth term of an arithmetic sequence:
a10 = a1 + (n - 1) * d
where:
a10 is the 10th term,
a1 is the first term,
n is the position of the term.
In this case, a1 is the 2nd term of the sequence, which is 28, and n is 10.
a10 = 28 + (10 - 1) * (-2)
a10 = 28 - 18
a10 = 10
Therefore, the 10th term of the linear sequence is 10.
To find the 10th term of a linear sequence, we need to determine the common difference (d) between consecutive terms. The common difference is the amount by which each term increases or decreases.
Given that the 2nd term is 28 and the 17th term is -2, we can find the common difference by subtracting the 2nd term from the 17th term and dividing it by the number of terms between them.
Common difference (d) = (17th term - 2nd term) / (17 - 2)
= (-2 - 28) / (17 - 2)
= -30 / 15
= -2
Now that we know the common difference (d = -2), we can find the 10th term using the formula for the nth term of a linear sequence: An = A1 + (n - 1)d.
In this formula, A1 represents the first term, n represents the position of the term we want to find, and d is the common difference.
For the given sequence, A1 is the 2nd term, which is 28. Plugging the values into the formula, we can calculate the 10th term:
A10 = A1 + (10 - 1)d
= 28 + (10 - 1)(-2)
= 28 + 9(-2)
= 28 + (-18)
= 10
Therefore, the 10th term of the linear sequence is 10.