Number Sequences and Patterns Flashcards

An electrician is installing light fixtures in a hallway. The fixtures are placed at the following distances from the start of the hallway (in feet): 4, 11, 18, 25. If this pattern continues, what is the distance of the next fixture?

Answer: 32 feet

This is an arithmetic sequence. The distance between each fixture is constant. 11 - 4 = 7; 18 - 11 = 7; 25 - 18 = 7. The pattern is to add 7 feet for each subsequent fixture. Therefore, the next fixture will be at 25 + 7 = 32 feet.

A motor's speed increases in a specific pattern every second. Its rotations per minute (RPM) are recorded as follows: 3, 9, 27, 81. What will the RPM be at the next second?

Answer: 243

This is a geometric sequence where each term is found by multiplying the previous term by a constant number. 9 / 3 = 3; 27 / 9 = 3; 81 / 27 = 3. The pattern is to multiply the RPM by 3 each second. The next value is 81 * 3 = 243.

What is the next number in the following sequence: 5, 10, 7, 12, 9, 14, ...?

Answer: 11

This sequence contains two separate, alternating patterns. The first pattern starts with 5 and adds 2 to every other number (5, 7, 9, ...). The second pattern starts with 10 and adds 2 to every other number (10, 12, 14, ...). The next number needed is part of the first pattern (9 + 2 = 11).

Identify the next number in this pattern: 2, 3, 5, 8, 12, ...

Answer: 17

The pattern in this sequence is based on an increasing difference between consecutive numbers. The difference between 2 and 3 is +1. The difference between 3 and 5 is +2. The difference between 5 and 8 is +3. The difference between 8 and 12 is +4. The next difference should be +5, so 12 + 5 = 17.

An electrical component's resistance is being reduced in fractional steps. Which fraction continues the pattern: 1/2, 3/4, 5/6, 7/8, ...?

Answer: 9/10

This sequence has two distinct patterns for the numerators and denominators. The numerators are consecutive odd numbers (1, 3, 5, 7, ...), so the next numerator is 9. The denominators are consecutive even numbers (2, 4, 6, 8, ...), so the next denominator is 10. The next fraction in the sequence is 9/10.

An apprentice is tasked with sorting and labeling wires. On day one, they label 6 circuits. On day two, they label 11 circuits. On day three, they label 16 circuits. If this rate of improvement continues, how many circuits will they label on the fifth day?

Answer: 26

The number of circuits labeled each day forms an arithmetic sequence. The difference between day two and day one is 11 - 6 = 5. The difference between day three and day two is 16 - 11 = 5. The pattern is an increase of 5 circuits per day. Day 4 would be 16 + 5 = 21 circuits. Day 5 would be 21 + 5 = 26 circuits.