Math Lesson 5: Number Patterns

Introduction to Patterns

Number patterns are sequences that follow a specific rule, such as adding, subtracting, or multiplying by a constant value to find the next term.

What is the next number in the sequence: 1, 3, 5, 7, ...?

In an arithmetic sequence, the difference (d) between terms is constant.
Formula: $T_n = a + (n - 1)d$

Find the 10th term of the sequence: 3, 7, 11, 15...

A quadratic sequence has a constant second difference.
Formula: $T_n = an^2 + bn + c$

For the sequence 2, 6, 12, 20..., determine the coefficients:

$T_n =$ $n^2 +$ $n +$

In a geometric sequence, each term is found by multiplying the previous term by a constant ratio (r).
Formula: $T_n = a \cdot r^{n-1}$

Find the 7th term of the sequence: 2, 6, 18, 54...

A series is the sum of the terms of a sequence. We use $S_n$ to represent the sum of the first $n$ terms.

Sum of the first 12 terms of 2 + 5 + 8 + ...?

Confused by a complex sequence? Ask our AI assistant for a step-by-step breakdown: