Answer:
First term: 3
Common difference: -1
Explanation:
3rd term: 1
6th term: x
10th term: 3x
Formula for the nth term using the common difference d and the first term a1:
an = a1 + (n - 1)d
Third term: a3 = a1 + (3 - 1)d = a1 + 2d = 1
6th term: a6 = a1 + (6 - 1)d = a1 + 5d = x
10th term: a10 = a1 + (10 - 1)d = a1 + 9d = 3x
a1 + 2d = 1 Eq. 1
a1 + 5d = x Eq. 2
a1 + 9d = 3x Eq. 3
Eq. 2 - Eq. 1
3d = x - 1
Eq. 3 - Eq. 2
4d = 2x
x = 2d
3d = x - 1
Substitute 2d for x.
3d = 2d - 1
d = -1
a1 + 2d = 1
a1 + 2(-1) = 1
a1 = 3
Check:
Here are the first 10 terms:
3, 2, 1, 0, -1, -2, -3, -4, -5, -6
The third term is 1. Correct
The tenth term (-6) is 3 times the 6th term (-2). Correct
Answer:
First term: 3
Common difference: -1