The 8th term of a linear sequence is 18th and the 12th term is 26th .find the first term,common difference and the 20th term

a+7d = 18

a+11d = 26
subtract them:
4d = 8
d = 2

in a+7d = 18
2+7d = 18

carry on

Your question does not make sense

"The 8th term of a linear sequence is 18th"
= gobbledegoop!
In any arithmetic (linear) sequence, the terms either increase or decrease. A term can never repeat itself
if you meant:
The 8th term of a linear sequence is 18 , we can do something

Correct your question, and we'll go from there.

To find the first term, common difference, and the 20th term of the linear sequence, we can use the formulas for arithmetic sequences.

Let's first find the common difference (d):

d = (term[n] - term[m]) / (n - m)

where term[n] represents the nth term of the sequence.

Given:
term[8] = 18
term[12] = 26

Using the formula, we can calculate the common difference:

d = (term[12] - term[8]) / (12 - 8)
d = (26 - 18) / 4
d = 8 / 4
d = 2

So, the common difference (d) is 2.

Now, let's find the first term (a). We can use the formula:

a = term[n] - (n - 1) * d

Using the value from term[8]:

a = term[8] - (8 - 1) * d
a = 18 - 7 * 2
a = 18 - 14
a = 4

So, the first term (a) is 4.

To find the 20th term (term[20]), we can use the formula:

term[n] = a + (n - 1) * d

Substituting the values we found:

term[20] = 4 + (20 - 1) * 2
term[20] = 4 + 19 * 2
term[20] = 4 + 38
term[20] = 42

So, the 20th term of the sequence is 42.

In summary:
First term (a) = 4
Common difference (d) = 2
20th term (term[20]) = 42

To find the first term, common difference, and 20th term of the linear sequence, we need to use the formulas for arithmetic sequences.

An arithmetic sequence is defined by the formula:

\[a_n = a_1 + (n-1)d\]

Where:
- \(a_n\) represents the \(n\)th term of the sequence.
- \(a_1\) represents the first term of the sequence.
- \(d\) represents the common difference of the sequence.

Let's calculate the values step by step:

Step 1: Finding the common difference (d)
We have two equations using the information given:
\(a_8 = 18\) and \(a_{12} = 26\).

Using the formula for the \(n\)th term of an arithmetic sequence, we can set up two equations:

\[a_8 = a_1 + (8-1)d = 18, \quad \text{(equation 1)}\]
\[a_{12} = a_1 + (12-1)d = 26, \quad \text{(equation 2)}\]

Subtracting equation 1 from equation 2 eliminates the first term:

\[(a_1 + 11d) - (a_1 + 7d) = 26 - 18\]
\[4d = 8\]
\[d = 2\]

So, the common difference (d) is 2.

Step 2: Finding the first term (a_1)
We can substitute the value of the common difference (d) into equation 1:

\[a_8 = a_1 + (8-1)2 = 18\]
\[a_8 = a_1 + 14 = 18\]
\[a_1 = 18 - 14 = 4\]

The first term (a_1) is 4.

Step 3: Finding the 20th term (a_20)
Using the formula for the \(n\)th term of an arithmetic sequence, we substitute into the formula:

\[a_{20} = a_1 + (20-1)d = 4 + 19 \cdot 2 = 42\]

The 20th term (a_20) is 42.

To summarize:
- The first term (a_1) is 4.
- The common difference (d) is 2.
- The 20th term (a_20) is 42.