Sequences, Explicit & Recursive — Drills
Sequences, Explicit & Recursive has 8 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 7 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Ratio — A comparison of two quantities, like 3 cups flour to 2 cups water.
- Arithmetic sequence — A list that grows by adding the same amount each time.
- Domain — The set of allowed inputs.
- Sequence — An ordered list of numbers. The nth one is an.
- Explicit formula — A rule giving an directly from n.
- Recursive formula — A rule giving an from an-1, plus a starting value.
- Continuous — A function you could draw without lifting the pen — no holes, jumps or blow-ups.
Classifying
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Classify 6, 15, 24, 33, … as arithmetic or geometric.
Worked answer
arithmetic
Differences: 9, 9, 9
Ratios: 2.5, 1.6, 1.375
Constant difference 9, so arithmetic.
Problem 2
Classify 5, 10, 15, 20, … as arithmetic or geometric.
Worked answer
arithmetic
Differences: 5, 5, 5
Ratios: 2, 1.5, 1.3333333333333333
Constant difference 5, so arithmetic.
Term
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the 22th term of 7, 10, 13, ….
Worked answer
70
7 + 21(3)
= 70
Problem 2
Find the 4th term of 6, 12, 24, ….
Worked answer
48
6 · 23
= 48
Explicit
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Write an explicit formula for 9, 10, 11, 12, ….
Worked answer
a_n = 9 + 1(n - 1)
a1 = 9, d = 1
an = 9 + (n-1)(1)
Simplified: 1n + 8
Problem 2
Write an explicit formula for 12, 10, 8, 6, ….
Worked answer
a_n = 12 + -2(n - 1)
a1 = 12, d = -2
an = 12 + (n-1)(-2)
Simplified: -2n + 14
Recursive
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Write a recursive formula for 7, 28, 112, 448, ….
Worked answer
a_1 = 7, a_n = 4a_(n-1)
a1 = 7
an = 4an-1
Both lines are required.
Problem 2
Write a recursive formula for 6, 9, 12, 15, ….
Worked answer
a_1 = 6, a_n = a_(n-1) + 3
a1 = 6
an = an-1 + 3
Both lines are required.
Findd
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
An arithmetic sequence has a5 = 30 and a7 = 44. Find d.
Worked answer
7
44 - 30 = 14
14 ÷ 2 = 7
Problem 2
An arithmetic sequence has a3 = 20 and a9 = 56. Find d.
Worked answer
6
56 - 20 = 36
36 ÷ 6 = 6
Findr
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A geometric sequence has a2 = 24 and a5 = 1536. Find a1.
Worked answer
6
24 · r3 = 1536, so r3 = 64 and r = 4
a1 = 24 ÷ 4 = 6
Problem 2
A geometric sequence has a2 = 24 and a5 = 648. Find a1.
Worked answer
8
24 · r3 = 648, so r3 = 27 and r = 3
a1 = 24 ÷ 3 = 8
From a graph
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
The graph of a sequence is
- a set of separate points
- a continuous line
- a shaded region
- a smooth curve
Worked answer
a set of separate points
The domain is the counting numbers only.
So the graph is separate dots, never joined.
Sum
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
How many terms are there in 4, 11, 18, …, 144?
Worked answer
21
(n-1)(7) = 140
n - 1 = 20
n = 21
Problem 2
How many terms are there in 7, 13, 19, …, 67?
Worked answer
11
(n-1)(6) = 60
n - 1 = 10
n = 11