Explicit formula — Algebra I · Grade 9 or accelerated Grade 8, what it means and where it is taught
A rule giving an directly from n.
Taught in Algebra I · Grade 9 or accelerated Grade 8.
Where it is taught
Practise this idea
4 questions in the course bank use Explicit formula, in Writing & Transforming Linear Functions, Sequences, Explicit & Recursive.
Problem 1
Write an explicit formula for 8, 14, 20, 26, ….
Worked answer
a_n = 8 + 6(n - 1)
an = 8 + (n-1)6
Or equivalently 6n + 2
Problem 2
Write an explicit formula for 6, 10, 14, 18, ….
Worked answer
a_n = 6 + 4(n - 1)
an = 6 + (n-1)4
Or 4n + 2
Problem 3
Write an explicit formula for 80, 40, 20, 10, ….
Worked answer
a_n = 80(1/2)^(n-1)
an = 80(12)n-1
Problem 4
Write an explicit formula for the arithmetic sequence with a5 = 23 and a9 = 43.
Worked answer
a_n = 3 + 5(n - 1)
d = 43 - 234 = 5
a1 = 23 - 4(5) = 3
an = 3 + 5(n-1), or 5n - 2