Sequences & Number Patterns

Arithmetic sequence: Each term increases by a constant.

2, 5, 8, 11, 14... (common difference = 3)

nth term = first term + (n-1) x common difference

Sum of n terms = n x (first + last) / 2

Geometric sequence: Each term multiplied by a constant.

3, 6, 12, 24, 48... (common ratio = 2)

nth term = first term x ratio^(n-1)

GRE patterns:

Repeating cycles: "What is the 73rd digit of 0.142857142857...?"

The pattern repeats every 6 digits. 73 / 6 = 12 remainder 1. The 73rd digit = the 1st digit = 1.

Units digit patterns:

Powers of 2: 2, 4, 8, 6, 2, 4, 8, 6... (cycle of 4)

Powers of 3: 3, 9, 7, 1, 3, 9, 7, 1... (cycle of 4)

Find the remainder when dividing the exponent by the cycle length.

Reference:

Wikipedia: Arithmetic Progression

https://en.wikipedia.org/wiki/Arithmetic_progression