PISA-Aligned Test: Sequences and Patterns

An architect designs a staircase where each step is 2 cm higher than the previous one. The first step is 12 cm high. What is the height of the 8th step?

• 24 cm

• 26 cm

• 28 cm

• 30 cm

Answer explanation

Arithmetic sequence with first term a₁ = 12 cm and common difference d = 2 cm.
n-th term: aₙ = a₁ + (n − 1)d = 12 + (8 − 1)·2 = 12 + 14 = 26 cm.

A tile pattern is formed by arranging triangles: - 1st figure: 3 triangles - 2nd figure: 6 triangles - 3rd figure: 9 triangles How many triangles will be in the 10th figure?

• 30

• 27

• 33

• 36

Answer explanation

Number of triangles increases by 3 each figure: 3, 6, 9, ... (d = 3).
10th figure: a₁₀ = 3 × 10 = 30.

Liza jogs 1 km on the first day, then increases her distance by 0.5 km every day. On which day will she first jog 5 km or more?

Answer explanation

Distances form aₙ = 1 + 0.5(n − 1).
Find smallest n such that aₙ ≥ 5:
1 + 0.5(n − 1) ≥ 5 ⇒ 0.5(n − 1) ≥ 4 ⇒ n − 1 ≥ 8 ⇒ n ≥ 9.

A row of benches in a school yard is arranged so that the 1st row has 4 benches, the 2nd row has 7 benches, the 3rd row has 10 benches, and so on. How many benches are in the 12th row?

Look at this sequence of shapes: 🔺 🔺🔺 🔺🔺🔺 🔺🔺🔺🔺 How many triangles are in the 20th figure?

• 100

• 200

• 210

• 400

A mobile plan gives 2 GB of data in the 1st month, and each month the data allowance increases by 1.5 GB. How much total data will be received after 6 months?

A plant grows in height according to this pattern: - Week 1: 5 cm - Week 2: 8 cm - Week 3: 11 cm Write a formula to find the plant's height in week n.

In a theater, the 1st row has 20 seats, the 2nd row has 24 seats, the 3rd row has 28 seats, and so on. How many seats are there in the 15th row?

A tank is filled with water in a sequence: - 1st minute: 2 liters - 2nd minute: 4 liters - 3rd minute: 8 liters - 4th minute: 16 liters If the pattern continues, how much water will be added in the 7th minute?

Carlo saves money in a sequence: - 1st week: ₱100 - 2nd week: ₱150 - 3rd week: ₱200 - 4th week: ₱250 How much money will Carlo have saved in total after 10 weeks?