The third and eight term of an Arithmetic progression are -9 and 26 respectively,find the common difference
The first term in the sequence is 37. The common difference is -3. Part A: What is the next three terms
a+2d = -9
a+7d = 26
so, 5d = 35
d = 7
I still don't understand
To find the common difference of an arithmetic progression, we need to use the formula:
an = a + (n-1)d
Where:
an is the nth term of the arithmetic progression,
a is the first term of the arithmetic progression, and
d is the common difference.
Given that the third term (a3) is -9 and the eighth term (a8) is 26, we can substitute these values into the formula:
a3 = a + (3-1)d => -9 = a + 2d
a8 = a + (8-1)d => 26 = a + 7d
Now we have a system of two equations with two unknowns (a and d). We can solve this system of equations to find the value of d.
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
From equation 1, we can isolate 'a' in terms of 'd':
a = -9 - 2d
Substitute this value of 'a' into equation 2:
26 = (-9 - 2d) + 7d => 26 = -9 + 5d => 35 = 5d => d = 7
Therefore, the common difference of the arithmetic progression is 7.