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

To find the common difference, 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:

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

Similarly, for the 12th term being 20:

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, we get:

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

So, the common difference is 0.5.

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

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

We can substitute the value of A1 from the first equation:

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

Now we can find the 20th term:

A20 = 14.5 + 9.5
A20 = 24

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