The 8th term if a linear sequence id 18 and the 12th term is 26. Find

Question

The first term
The common difference
The20t

Answer 1

To find the first term and the common difference of the linear sequence, we can use the formula for the nth term of an arithmetic 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 and the 12th term is 26, we can set up two equations using the formula:

18 = A1 + 7d (for the 8th term)
26 = A1 + 11d (for the 12th term)

Now, we can solve these two equations simultaneously to find A1 and d.

Subtract the first equation from the second equation:

26 - 18 = A1 + 11d - (A1 + 7d)
8 = 4d

Divide by 4:

d = 2

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

18 = A1 + 7(2)
18 = A1 + 14
A1 = 4

Therefore, the first term is 4 and the common difference is 2.

To find the 20th term, we can plug in n = 20 into the formula:

A20 = 4 + (20-1)(2)
A20 = 4 + 19(2)
A20 = 4 + 38
A20 = 42

Therefore, the 20th term of the linear sequence is 42.