The 8 term of a linear sequence is 18 and the 12th term 20 find the first term ?

To find the first term of the linear sequence, we can use the formula for the nth term of a linear sequence:

a_n = a_1 + (n-1)d

where:
a_n = the nth term of the sequence
a_1 = the first term of the sequence
d = the common difference between terms
n = the term number

Given that the 8th term is 18 and the 12th term is 20, we can set up two equations using the formula above:

18 = a_1 + (8-1)d
20 = a_1 + (12-1)d

Solving these two equations simultaneously, we get:

18 = a_1 + 7d
20 = a_1 + 11d

Subtracting the first equation from the second equation, we get:

2 = 4d

Dividing by 4 on both sides, we get:

d = 0.5

Now, substitute the value of d back into the first equation:

18 = a_1 + 7(0.5)
18 = a_1 + 3.5
a_1 = 18 - 3.5
a_1 = 14.5

Therefore, the first term of the linear sequence is 14.5.