The 8th term of a linear sequence is 18th and 12th term is 26.find the first term and the common difference and 2th term

what is the 8th term of 200 100 50 25

Good.

To find the first term (a) and the common difference (d) of a linear sequence, we can set up a system of equations using the given information.

We are given two equations:

1) The 8th term is 18th.
a + 7d = 18 (since the 8th term can be represented as a + 7d)

2) The 12th term is 26.
a + 11d = 26 (since the 12th term can be represented as a + 11d)

To find the values of a and d, we need to solve this system of equations.

Subtracting equation 1) from equation 2), we get:

(a + 11d) - (a + 7d) = 26 - 18
4d = 8
d = 2

Now that we have the value of d, we can substitute it into equation 1) to find the value of a:

a + 7(2) = 18
a + 14 = 18
a = 18 - 14
a = 4

So, the first term (a) is 4 and the common difference (d) is 2.

To find the 2nd term, we can use the formula for the nth term of a linear sequence:

nth term = a + (n - 1)d

Substituting the values for a and d, we get:

2nd term = 4 + (2 - 1)2
2nd term = 4 + 2
2nd term = 6

Therefore, the 2nd term of the linear sequence is 6.

a+7d = 18

a+11d = 26

Now you can find a and d, and any other terms.