the 8 term of a linear sequence is 18 and the 12 term is 26 find the first term common difference and the 20 term
Just use your definitions ....
"the 8 term of a linear sequence is 18" ----> a + 7d = 18
"the 12 term is 26" ----> a + 11d = 26
Now subtract them: 4d = 8
d = 4 , there! now you have your common difference
sub back into a+7d = 18 to find a
once you have a and d,
term( 20) = a + 19d = .....
To find the first term (a) and common difference (d) of a linear sequence, you can use the formula:
an = a + (n-1)d
where an represents the term at position n.
Let's use the given information to find a and d:
Given:
a8 = 18
a12 = 26
For a8, we have:
18 = a + (8-1)d
18 = a + 7d ----(1)
For a12, we have:
26 = a + (12-1)d
26 = a + 11d ----(2)
Now, we have a system of two equations with two variables (a and d). We can solve these equations simultaneously.
Subtract equation (1) from equation (2) to eliminate a:
26 - 18 = (a + 11d) - (a + 7d)
8 = 4d
d = 2
Now substitute the value of d into equation (1) to solve for a:
18 = a + 7(2)
18 = a + 14
a = 18 - 14
a = 4
So, the first term (a) of the sequence is 4 and the common difference (d) is 2.
To find the 20th term (a20), we can use the formula again:
a20 = a + (20-1)d
a20 = 4 + 19(2)
a20 = 4 + 38
a20 = 42
Therefore, the 20th term of the linear sequence is 42.
d = (26-18)/(12-8) = 2
a_20 = a_12 + 8d = 26+16 = 42