CBSE Class 9 Maths Ganita Manjari Part 1 Ch 08 Predicting What Comes Next Exploring Sequences and Progressions MCQs with Answers Set 01

Answer: (b) 33

Explanation:
1. This is an AP with a = 12 and d = 3.
2. \( a_8 = a + 7d = 12 + 7(3) = 33 \).

Answer: (a) \( 5n + 3 \)

Explanation:
1. a = 8 and d = 5, so \( a_n = 8 + (n - 1)5 = 5n + 3 \).
2. Check: n = 1 gives 8 and n = 2 gives 13 ✓.

Answer: (b) Each step has 3 more tiles than the previous one

Explanation:
1. 8 − 5 = 3 and 11 − 8 = 3.
2. The difference is always 3, so each step has 3 more tiles than the one before.

Answer: (b) 9th

Explanation:
1. a = 4 and d = 5. Solve \( 4 + (n - 1)5 = 44 \).
2. \( (n - 1)5 = 40 \Rightarrow n - 1 = 8 \Rightarrow n = 9 \).
3. So 44 is the 9th term.

Answer: (b) ₹400

Explanation:
1. a = 100 and d = 50.
2. \( a_7 = 100 + 6(50) = 400 \). So ₹400 is saved in the 7th week.

Answer: (c) Each term is doubled, so the terms grow much faster

Explanation:
1. Each term is twice the previous one (3 × 2 = 6, 6 × 2 = 12, …), so this is not an AP.
2. The 10th term is \( 3 \times 2^9 = 1536 \), far more than 30.
3. The student wrongly assumed the terms go up by 3 each time.

Answer: (a) \( n^2 + 1 \)

Explanation:
1. For n = 1, 2, 3, 4, 5: \( n^2 + 1 \) gives 2, 5, 10, 17, 26 ✓.
2. The other rules fail at once; for example, \( 2n + 1 \) gives 3 for n = 1.

Answer: (b) 21

Explanation:
1. \( a_{12} = 84 - 2 = 82 \) and \( a_9 = 63 - 2 = 61 \).
2. Difference = 82 − 61 = 21. (Or: 3 steps × d = 3 × 7 = 21.)

Answer: (d) 36

Explanation:
1. Every term is \( 4 + 5k \), so every term leaves remainder 4 when divided by 5 (ends in 4 or 9).
2. 24, 29 and 34 fit this pattern; 36 does not (36 − 4 = 32 is not a multiple of 5).

Answer: (c) 7th

Explanation:
1. \( 20 + (n - 1)(-3) = 2 \Rightarrow -3(n - 1) = -18 \Rightarrow n - 1 = 6 \).
2. n = 7, so 2 is the 7th term.

Answer: (b) 5

Explanation:
1. Common difference d = 17 − 11 = 6.
2. x = 11 − 6 = 5.

Answer: (c) 144

Explanation:
1. The terms are square numbers: the nth term is \( n^2 \).
2. 12th figure = \( 12^2 = 144 \) tiles.

Answer: (c) 4

Explanation:
1. From the 5th to the 9th term there are 4 steps: \( a_9 - a_5 = 4d \).
2. \( 4d = 34 - 18 = 16 \Rightarrow d = 4 \).

Answer: (b) 16, 19

Explanation:
1. Terms are 10, 13, 16, 19, 22, 25, … (n = 1, 2, 3, …), and consecutive terms always differ by 3.
2. 16 (n = 3) and 19 (n = 4) are consecutive terms.
3. The other pairs differ by 4, so they cannot be consecutive terms (13 is followed by 16, 19 by 22, and 22 by 25).

Answer: (b) Use the AP sum formula after finding the number of terms

Explanation:
1. a = 2, d = 3 and last term 29: \( 2 + (n - 1)3 = 29 \Rightarrow n = 10 \).
2. \( S_{10} = \frac{10}{2}(2 + 29) = 155 \). The formula avoids long addition.

Answer: (c) 10th

Explanation:
1. \( a_n = 50 - 5(n - 1) \).
2. \( a_9 = 50 - 40 = 10 \), which is not less than 10.
3. \( a_{10} = 50 - 45 = 5 \), which is the first term less than 10.

Answer: (c) 240

Explanation:
1. a = 6, d = 4 and n = 10.
2. \( S_{10} = \frac{10}{2}[2(6) + 9(4)] = 5 \times 48 = 240 \).

Answer: (a) Their corresponding terms differ by 5

Explanation:
1. The terms are 3, 7, 11, … and 8, 12, 16, … .
2. Both increase by the same amount, so the gap between matching terms stays 8 − 3 = 5 for ever.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. By definition, an AP has a constant common difference. The Assertion is true.
2. Adding the same number d each time is how an AP is formed, which is why consecutive terms always differ by d. The Reason is true and explains A.

Answer: (d) A is false, but R is true.

Explanation:
1. The differences are 6 − 2 = 4, 12 − 6 = 6, 20 − 12 = 8 and 30 − 20 = 10. The Reason is true.
2. The differences are not constant, so the sequence is not an AP. The Assertion is false.