Teachoo MCQ Test

10 Question MCQ (including Assertion)

Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress | 10 questions

Timed test. Answer every question before time runs out. Correct answers and solutions appear after submission.
Time remaining 960
Question 1 of 10
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Question 1 of 10
A Sierpiński square carpet begins with \(1\) red square at Stage \(0\). At each stage, every red square is replaced by \(8\) smaller red squares. How many red squares are present at Stage \(4\)?
Early stages of a Sierpiński square carpetStage zero is a solid square. Stage one has the centre ninth removed. Stage two repeats the removal in each retained square.Stage 0Stage 1Stage 2
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Question 2 of 10
For the Virahānka–Fibonacci sequence \(V_1=1\), \(V_2=2\), and \(V_n=V_{n-1}+V_{n-2}\), what is \(V_8\)?
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Question 3 of 10
The sequence is \(1, 4, 7, 10, 13, \ldots\). Which option gives the next four terms?
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Question 4 of 10
Find the 3rd term (\(S_3\)) of the sequence given by the recursive rule \(S_1 = 3, S_n = S_{n-1}(S_{n-1} - 1)\) for \(n \ge 2\).
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Question 5 of 10
The Stage \(0\) Sierpiński square carpet has area \(1\) square unit. At each stage, \(\dfrac89\) of the previous red area remains. What is the red area at Stage \(3\)?
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Question 6 of 10
What is the explicit formula for the AP \(11,8,5,2,\ldots\)?
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Question 7 of 10
For the sequence defined by \(t_n=3n-7\), what is \(t_{18}\)?
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Question 8 of 10
Assertion: If the ordered pairs \((n,t_n)\) of an AP are plotted, the points lie on a straight line.
Reason: Every arithmetic progression has a constant ratio between consecutive terms.
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Question 9 of 10
An AP consists of 50 terms in which the 3rd term is 12 and the last term is 106. Find the common difference \(d\).
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Question 10 of 10
Which sequence is a geometric progression with common ratio \(\dfrac23\)?
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