second term is 8 and fourth term is 14.find the first term and the common difference.
a+d = 8
a+3d = 14
subtract them:
2d = 6
d = 3
I will let you finish it
To find the first term and common difference in an arithmetic sequence, you need a formula that relates the terms of the sequence.
The formula for the nth term (Tn) of an arithmetic sequence is given by:
Tn = a + (n-1)d
Where:
Tn = nth term
a = first term
d = common difference
n = position of the term in the sequence
Given that the second term (n = 2) is 8 and the fourth term (n = 4) is 14, we can substitute these values into the formula to set up two equations:
For the second term (n = 2):
8 = a + (2-1)d
8 = a + d
For the fourth term (n = 4):
14 = a + (4-1)d
14 = a + 3d
Now we have a system of equations:
Equation 1: a + d = 8
Equation 2: a + 3d = 14
We can solve this system of equations to find the values of a and d.
Subtracting Equation 1 from Equation 2, we get:
(a + 3d) - (a + d) = 14 - 8
2d = 6
d = 3
Substituting the value of d into Equation 1, we can find a:
a + 3 = 8
a = 5
Therefore, the first term (a) is 5 and the common difference (d) is 3.