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

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

An = A1 + (n-1)d

where An is the nth term, A1 is the first term, n is the term number, and d is the common difference.

Given that the 8th term is 18, we can plug in the values into the formula:

18 = A1 + (8-1)d
18 = A1 + 7d

Similarly, given that the 12th term is 20, we can plug in the values into the formula:

20 = A1 + (12-1)d
20 = A1 + 11d

Now we have a system of two equations:

18 = A1 + 7d
20 = A1 + 11d

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

20 - 18 = (A1 + 11d) - (A1 + 7d)
2 = 4d
d = 2/4
d = 0.5

Now that we have found the common difference, we can substitute it back into one of the equations to find the first term:

18 = A1 + 7(0.5)
18 = A1 + 3.5
A1 = 18 - 3.5
A1 = 14.5

Therefore, the first term is 14.5 and the common difference is 0.5.

To find the 20th term, we can use the formula:

A20 = A1 + (20-1)d
A20 = 14.5 + 19(0.5)
A20 = 14.5 + 9.5
A20 = 24

Therefore, the 20th term of the linear sequence is 24.