If the 6th term of an arithmetic sequence is 48, and the sum of the first 6 terms is 300, what is the first term and the constant difference?

just use your facts about such sequences:

a+5d = 48
6/2(a + a+5d) = 300

Now just solve for a and d.

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To find the first term and the constant difference of an arithmetic sequence, we can use the given information about the 6th term and the sum of the first 6 terms.

Let's denote the first term as 'a' and the constant difference as 'd'.

We are given that the 6th term is 48, which means:
a + 5d = 48 -- Equation 1

We are also given that the sum of the first 6 terms is 300, which can be calculated using the formula for the sum of an arithmetic sequence:
S = (n/2)(2a + (n - 1)d),
where S is the sum, n is the number of terms, a is the first term, and d is the constant difference.

Substituting the given values, we have:
300 = (6/2)(2a + (6 - 1)d)
300 = 3(2a + 5d)
100 = 2a + 5d -- Equation 2

Now, we have a system of equations (Equations 1 and 2) that we can solve simultaneously to find the values of 'a' and 'd'.

To solve the system of equations, we can use substitution or elimination method:

Let's use substitution method:
From Equation 2, we can solve for 'a' in terms of 'd':
2a = 100 - 5d
a = (100 - 5d)/2

Substituting this value of 'a' in Equation 1, we have:
(100 - 5d)/2 + 5d = 48
100 - 5d + 10d = 96
5d = -4
d = -4/5

Now, substituting the value of 'd' back into Equation 2, we can solve for 'a':
a = (100 - 5(-4/5))/2
a = (100 + 4)/2
a = 104/2
a = 52

Therefore, the first term (a) is 52 and the constant difference (d) is -4/5.