Patterns and Sequences Flashcards

What is the missing term: 100, 81, 64, ___, 36?

Answer: 49

These are perfect squares in decreasing order: 10², 9², 8², 7², 6²; the missing term is 7² = 49.

The rule for a sequence is: multiply the previous term by 2, then subtract 1. If the first term is 4, what is the 4th term?

Answer: 25

T1=4, T2=4×2−1=7, T3=7×2−1=13, T4=13×2−1=25.

How many terms are in the arithmetic sequence: 7, 11, 15, ..., 55?

Answer: 13

n = (last − first)/d + 1 = (55 − 7)/4 + 1 = 48/4 + 1 = 13.

A pattern shows triangular numbers: 1, 3, 6, 10, 15, ___. What is the next triangular number?

Answer: 21

Triangular numbers are 1, 3, 6, 10, 15, 21 — each adding the next natural number: +2, +3, +4, +5, +6.

The sum of an arithmetic series is given by S = n/2 (a + l). Find the sum of 1+2+3+...+100.

Answer: 5050

S = 100/2 × (1 + 100) = 50 × 101 = 5050.

In a sequence 2, x, 18, 54, ..., what is the value of x if this is a geometric sequence?

Answer: 6

Common ratio r = 54/18 = 3; so x = 2 × 3 = 6.