Sequences and formulas

Find the nth term.

Patterns in tiles

Tile patterns grow in regular ways. We can write a rule to find any step. This rule is called the nth term.

Linear sequences

The terms go up by 3, so the rule starts with 3n. 3 × 1 = 3, but the first term is 5: add 2. nth term = 3n + 2. The 10th term is 32.

Special sequences

Square numbers: 1, 4, 9, 16, 25 … Triangular numbers: 1, 3, 6, 10, 15 … Next triangular number: 21.

Formulas

A formula is a rule with letters. Substitute the number and calculate. C = 12n: for 5 pens, C = ৳60.

Solving equations

An equation is balanced: do the same to both sides. Subtract 5: 3n = 21. Divide by 3: n = 7. Write equations for word problems: “3 tickets and a ৳5 snack cost ৳26” → 3n + 5 = 26.

What I learnt

I can find the nth term of a linear sequence.
I know square and triangular numbers.
I can use simple formulas.