Answer:
-8, -4, 0, 4, 8, 12
Step-by-step explanation:
The nth term Tn of an arithmetic sequence with a common difference d and a first term a is given as
Tn = a + (n - 1) d
Hence if the first term is a and the common difference is d then
the
2nd term = a + 4
3rd term = a + (3 - 1) 4 = a + 8
4th term = a + (4 - 1) 4 = a + 12
5th term = a + (5 - 1) 4 = a + 16
6th term = a + (6 - 1) 4 = a + 20
If the sum of these six numbers is 12 then
a + a + 4 + a + 8 + a + 12 + a + 16 + a + 20 = 12
6a + 60 = 12
collect like terms
6a = 12 - 60
6a = -48
divide both sides by 6
a= -8
the numbers are
a = -8
2nd term = a + 4 = -8 + 4 = -4
3rd term = a + (3 - 1) 4 = a + 8 = -8 + 8 = 0
4th term = a + (4 - 1) 4 = a + 12 = -8 + 12 = 4
5th term = a + (5 - 1) 4 = a + 16 -8 + 16 = 8
6th term = a + (6 - 1) 4 = a + 20 = -8 + 20 = 12
