Class 6 Computational Thinking & AI
Official CBSE Student Handbook curriculum with 280 interactive practice questions (20 questions per chapter), triangular numbers, line angle kinematics, Turing test concepts, and step-by-step logic solutions.
Patterns in Mathematics
Patterns in Mathematics explores algebraic sequences, polynomial differences, 2D tile growth algorithms, and set permutation invariants.
Practice Questions (20)
Click an option to test your solutionThe series follows a fixed pattern: 2 (1 time), 3 (2 times), 4 (3 times), 5 (4 times), 6 (5 times), 7 (6 times)... where each integer 'n' appears (n − 1) times. In the NEXT 20 terms after 6 (which begins at 6), how many times does the number 9 appear?
Hint: Count the remaining slots in the 20-term window after 6s, 7s, and 8s.
Identify the INCORRECT term in the series: 2, 3, 6, 11, 18, 25, 38, 51, 66, 83.
Hint: The differences are consecutive odd numbers: +1, +3, +5, +7, +9...
Series: 1@3, #5#, 7@9, #11#, 13@15, [ ? ], 19@21. What replaces '?'?
Hint: The sequence is 1,3 → 5 → 7,9 → 11 → 13,15 → 17 → 19,21 with alternating symbols.
A block pyramid series has terms: Term 1 = 1 block, Term 2 = 1+2 = 3 blocks, Term 3 = 1+2+3 = 6 blocks, Term 4 = 1+2+3+4 = 10 blocks (Triangular numbers T_n = n(n+1)/2). Which term is the FIRST to contain MORE THAN 20 blocks?
Hint: Calculate triangular numbers: T_5 = 15, T_6 = 21.
Matrix pattern: [1,2 / 2,3], [2,3 / 3,4], [3,4 / 4,5], [4,5 / 5,6], [ ? ]. What matrix comes next?
Hint: Add 1 to each entry of [4,5 / 5,6].
Stacked numbers: (Top, Middle, Bottom): • Term 1: (3, 7, 4) → 3+4 = 7 • Term 2: (6, 11, 5) → 6+5 = 11 • Term 3: (9, 16, 7) → 9+7 = 16 • Term 4: (12, 22, 10) → 12+10 = 22 • Term 5: (15, 29, 14) → 15+14 = 29 What will replace '?' in Term 6?
Hint: Top = 18, Bottom = 19, Middle = 18 + 19 = 37.
In a hexagonal lattice pattern with grey hexagons and white diamonds: In term n, number of hexagons = n² and number of diamonds = (n − 1)². In the term where the number of hexagons is 144 (n² = 144 → n = 12), how many diamonds are present?
Hint: n = 12. Diamonds = (12 − 1)² = 11² = 121.
Two sets: Set P = {18, 22, 24, 27, 30} (multiples of 3 with one intruder 22) and Set Q = {21, 24, 27, 31, 36} (series with difference pattern). Which number from Set P can be interchanged with a number from Set Q so both sets follow regular mathematical patterns?
Hint: 22 is not a multiple of 3 in Set P. Swap 22 with 21.
Circles in interconnected chain: Term 1 = 6 circles, Term 2 = 8 circles (+2), Term 3 = 10 circles (+2). Formula for Term n = 2n + 4. How many circles will be in Term 91?
Hint: Term 91 = 2(91) + 4 = 182 + 4 = 184.
A cube pyramid has 2 fewer cubes at each higher level. Using AT MOST 30 cubes, what is the MAXIMUM number of levels it can have?
Hint: 1 + 3 + 5 + 7 + 9 = 25 cubes (5 levels).
Find the next term in the arithmetic sequence: 7, 14, 21, 28, ___
Hint: Multiples of 7: 7 × 5 = 35.
What is the 10th term of the sequence of square numbers (1, 4, 9, 16...)?
Hint: 10 × 10 = 100.
What is the rule for the geometric sequence: 3, 9, 27, 81?
Hint: 3 × 3 = 9, 9 × 3 = 27.
Find the missing term: 100, 95, 90, 85, ___
Hint: Subtract 5 from 85.
How many terms are in the finite sequence: 5, 10, 15, ..., 50?
Hint: 50 ÷ 5 = 10.
What is the sum of the first 5 positive odd integers (1 + 3 + 5 + 7 + 9)?
Hint: 5² = 25.
Find the next letter in the pattern: B, D, F, H, ___
Hint: Skip one letter: H → (skip I) → J.
If the pattern is 'Multiply by 2 and add 1', what is the term after 15?
Hint: 15 × 2 + 1 = 31.
What is the 8th triangular number (T_8)?
Hint: 8 × 9 ÷ 2 = 36.
Find the missing number: 2, 6, 12, 20, 30, ___
Hint: 6 × 7 = 42.
The Thinking Spot: Box Item Elimination Shoot
Three boxes A, B, C contain shapes. Shooting 1 item in a box eliminates that item in its own box AND also eliminates identical copies of that item in the immediately adjacent box. You have exactly 3 shots (1 shot per box).
Question: What is the MAXIMUM number of items that can be eliminated after all 3 shots?