The eighth term of a linear sequence is 18 and twelveth term is 26.Find the first term,common difference and 20th term
18 to 26 is 4 terms with a difference of 8
... so the common difference is ... 8 / 4 = ?
the 20th term is 8 terms beyond 26 (the 12th term)
... 26 + 8 differences = ?
plz answer quick
if you labeled this a math question, it might have been answered sooner
To find the first term, common difference, and 20th term of a linear sequence, we need to use the formula for the nth term of an arithmetic sequence:
nth term = a + (n-1)d
where "a" is the first term, "d" is the common difference, and "n" is the term number.
Given that the 8th term is 18 and the 12th term is 26, we can substitute these values into the formula and set up two equations:
For the 8th term:
18 = a + (8-1)d
For the 12th term:
26 = a + (12-1)d
Simplifying these equations, we get:
18 = a + 7d ----(1)
26 = a + 11d ----(2)
Now we have a system of equations. We can solve it using algebraic methods.
Subtracting equation (1) from equation (2), we get:
26 - 18 = (a + 11d) - (a + 7d)
8 = 4d
d = 2
Plugging the value of d back into equation (1), we get:
18 = a + 7(2)
18 = a + 14
a = 4
Therefore, the first term (a) is 4 and the common difference (d) is 2.
Now let's find the 20th term using the formula:
nth term = a + (n-1)d
Substituting a = 4, d = 2, and n = 20, we have:
20th term = 4 + (20-1)2
20th term = 4 + 19(2)
20th term = 4 + 38
20th term = 42
So, the 20th term of the linear sequence is 42.