Question

What is the general rule for the arithmetic sequence? 15, 12, 9, 6, … A. 3n – 18 B. 6(3 – n) C. 3n + 12 D. 18 – 3n

Answer 1

A1 = first term
a1 = 15
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d = common difference 
d = (second term) - (first term)
d = a2 - a1
d = 9-12
d = -3
The negative common difference indicates that the terms are decreasing
Each time we subtract 3, or add -3, to get the next term.
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nth term of arithmetic sequence
an = a1 + d(n-1)
an = 15 + (-3)(n-1)
an = 15- 3n + 3
an = 18 - 3n

Answer is choice D