The 8th term of a linear sequence is 18 and the 12th term is 26 find the different between the 10th term and the 4th
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Answer
The 8th term of a linear sequence is 18 and the 12th term is 26
--->
a + 7d = 18
a + 11d = 26
subtract them:
4d = 8
d = 1/2
back into the first:
a + 7(1/2) = 18
solve for a
then find
(a+9d) - (a+3d) = .....
To find the difference between the 10th term and the 4th term of a linear sequence, we first need to determine the common difference between consecutive terms.
The formula for finding the nth term of a linear sequence is given by:
nth term = a + (n - 1)d
where "a" represents the first term, "n" represents the term number, and "d" represents the common difference.
In this case, we are given the values of the 8th term and the 12th term. Let's use this information to find the common difference (d).
Given:
8th term = 18 (term number = 8)
12th term = 26 (term number = 12)
Using the formula, we can set up two equations:
18 = a + (8 - 1)d (equation 1)
26 = a + (12 - 1)d (equation 2)
Now, we can solve these two equations simultaneously to find the values of "a" and "d".
Subtracting equation 1 from equation 2, we get:
26 - 18 = a + (12 - 1)d - (a + (8 - 1)d)
Simplifying, we have:
8 = a + 11d - a - 7d
Combining like terms:
8 = 4d
Dividing both sides by 4, we find:
d = 2
Now that we have the value of the common difference (d = 2), we can find the 10th term and the 4th term.
To find the 10th term, we substitute the values into the formula:
10th term = a + (10 - 1)d
Plugging in d = 2, we have:
10th term = a + (9)(2)
To find "a", we need to plug in one of the given terms. Let's use the 8th term:
18 = a + (8 - 1)(2)
Simplifying, we have:
18 = a + 7(2)
18 = a + 14
Subtracting 14 from both sides, we find:
4 = a
Now, substituting back into the equation for the 10th term, we have:
10th term = 4 + (9)(2)
10th term = 4 + 18
10th term = 22
Similarly, to find the 4th term:
4th term = a + (4 - 1)d
4th term = 4 + (3)(2)
4th term = 4 + 6
4th term = 10
Finally, we can find the difference between the 10th term and the 4th term:
Difference = 10th term - 4th term
Difference = 22 - 10
Difference = 12
Therefore, the difference between the 10th term and the 4th term is 12.