the 8th of a linear sequence is 18 and the 12 term is 26 find the first term of the common difference and 20th term
since the two given terms are four apart, d = (26-18)/4 = 2
so now you know that
a = 18 - 7*2 = 4
and a_20 = a+19d = _____
55 durbah ground
To find the first term and the common difference of the linear sequence, we can use the formula for the nth term of a linear sequence:
n-th term = first term + (n-1) * common difference
Given that the 8th term is 18 and the 12th term is 26, we can solve for the first term and the common difference.
1. Finding the common difference:
Using the formula for the 8th term:
18 = first term + (8-1) * common difference
Simplifying this equation:
18 = first term + 7 * common difference
Now, we can use the formula for the 12th term:
26 = first term + (12-1) * common difference
Simplifying this equation:
26 = first term + 11 * common difference
Now, we have a system of two equations:
18 = first term + 7 * common difference
26 = first term + 11 * common difference
By solving this system of equations, we can find the common difference.
Subtracting the first equation from the second equation, we get:
26 - 18 = (first term + 11 * common difference) - (first term + 7 * common difference)
8 = 4 * common difference
Divide both sides by 4:
common difference = 2
Therefore, the common difference of the sequence is 2.
2. Finding the first term:
Now that we have the common difference, we can substitute it back into one of the equations to find the first term. Let's use the first equation:
18 = first term + 7 * 2
Simplifying this equation:
18 = first term + 14
Subtracting 14 from both sides:
first term = 18 - 14
first term = 4
Therefore, the first term of the sequence is 4.
3. Finding the 20th term:
Using the formula for the nth term, we can substitute the values we found:
20th term = first term + (20-1) * common difference
20th term = 4 + 19 * 2
Simplifying this equation:
20th term = 4 + 38
20th term = 42
Therefore, the 20th term of the sequence is 42.