Exercises: Number Patterns and Sequences

Work through each section in order. Show your work where indicated. For arithmetic sequences, use the nth-term formula $a + (n-1)d$ .

Grade 7·18 problems·~30 min·Uganda NCDC Primary 7 Mathematics·lesson·patterns-03

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Recall / Warm-Up

These problems review sequence work you have already met.

Look at the sequence $3, 7, 11, 15, \ldots$ . What is the rule that gives each term from the one before it?

Add 4 each time.

Multiply by 2 each time.

Add 3 each time.

The sequence $2, 4, 6, 8, \ldots$ lists the even numbers in order. What is the next term?

Is the sequence $2, 4, 8, 16, \ldots$ arithmetic or geometric?

Geometric — each term is multiplied by 2, so the ratio is constant.

Arithmetic — the first gap is 2, so the common difference is 2.

Arithmetic — the terms increase, so a fixed amount is added.

In the sequence $4, 9, 14, \underline{\phantom{0}}, 24, \ldots$ the rule is 'add 5'. What is the missing term?

$Four triangular dot patterns with 1, 3, 6, and 10 dots, showing the triangular number sequence.$

The dot patterns below show the triangular numbers $1, 3, 6, 10, \ldots$ . What is the next triangular number after $10$ ?

For the arithmetic sequence $2, 5, 8, 11, \ldots$ (first term $a = 2$ , common difference $d = 3$ ), use $a + (n-1)d$ to find the 5th term.

For the arithmetic sequence $5, 8, 11, 14, \ldots$ (first term $a = 5$ , common difference $d = 3$ ), use $a + (n-1)d$ to find the 20th term.

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