The 8th term of linear sequence is 18 and the 12th term is 26.find the first term, the common difference and the 20th term
Pls I want solution to the question
d = (26-18)/(12-8) = ____
now you have d, so
a = 18 - 7d
Now you have a and d, so
a20 = a+19d
Of course, you don's need a and d to find a20
since the 20th term is 8 terms past the 12 term, which is 4 terms past the 8th term, it is twice as far from a12 as a12 is from a8.
a20 = 26 + 2(26-18) = ____
To find the first term, common difference, and the 20th term of a linear sequence, we need to use the formula for the nth term of an arithmetic sequence.
The formula is:
An = A1 + (n - 1)d
where An represents the nth term, A1 represents the first term, n represents the term number, and d represents the common difference.
Given that the 8th term is 18 and the 12th term is 26, we can substitute these values into the formula to form two equations:
18 = A1 + (8 - 1)d -- (equation 1)
26 = A1 + (12 - 1)d -- (equation 2)
Now we can solve these two equations simultaneously to find the values of A1 (the first term) and d (the common difference).
First, let's solve for A1 by eliminating the d term. We can subtract equation 1 from equation 2:
26 - 18 = A1 + (12 - 1)d - (A1 + (8 - 1)d)
8 = A1 + 11d - A1 - 7d
8 = 4d
Dividing both sides by 4 gives us:
d = 2
Now that we have the value of d, we can substitute it back into either equation 1 or equation 2 to solve for A1.
Let's choose equation 1:
18 = A1 + (8 - 1)2
18 = A1 + 7(2)
18 = A1 + 14
A1 = 18 - 14
A1 = 4
So, the first term (A1) is 4 and the common difference (d) is 2.
To find the 20th term, we can use the same formula:
A20 = A1 + (20 - 1)d
A20 = 4 + 19(2)
A20 = 4 + 38
A20 = 42
Therefore, the 20th term of the linear sequence is 42.