Series & Sigma Notation — Drills
Series & Sigma Notation has 6 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 5 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.
- Common difference — The constant added each time, in an arithmetic sequence.
- Common ratio — The constant multiplied each time, in a geometric sequence.
- Series — The sum of the terms of a sequence.
- Limit — The value a function approaches as the input approaches some number.
Sigma
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Evaluate ∑k=15 (4k+6).
Worked answer
90
Terms: 10, 14, 18, 22, 26
Total =90
Problem 2
Evaluate ∑k=16 (3k+2).
Worked answer
75
Terms: 5, 8, 11, 14, 17, 20
Total =75
Arith
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the sum of the first 25 terms of 5, 11, 17, …
Worked answer
1925
a25=5+24(6)=149
252(5+149)=1925
Problem 2
Find the sum of the first 15 terms of 7, 12, 17, …
Worked answer
630
a15=7+14(5)=77
152(7+77)=630
Terms
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
How many terms are there from 6 to 50 counting by 4?
Worked answer
12
50-64=11 gaps
11+1=12 terms
Problem 2
How many terms are there from 8 to 36 counting by 4?
Worked answer
8
36-84=7 gaps
7+1=8 terms
Geom
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the sum of the first 4 terms of 6, 18, 54, …
Worked answer
240
Sn = 61-341-3
=6 · -80-2 = 240
Problem 2
Find the sum of the first 6 terms of 1, 3, 9, …
Worked answer
364
Sn = 11-361-3
=1 · -728-2 = 364
Ratio
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the common ratio of 81, 20.25, 5.0625, …
Worked answer
1/4
20.25 ÷ 81 = 14
Problem 2
Find the common ratio of 96, 32, 10.666666666666666, …
Worked answer
1/3
32 ÷ 96 = 13
Infinite
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the sum of the infinite series 12+3+0.75+⋯
Worked answer
16
r=14
S=121-14=16
Problem 2
Find the sum of the infinite series 4+2+1+⋯
Worked answer
8
r=12
S=41-12=8