Class 9 Predicting What Comes Next: Exploring Sequences and Progressions Mock Test (CBSE)

Topics in Predicting What Comes Next: Exploring Sequences and Progressions

• Sequences
• Explicit rule for a sequence
• Recursive rule for a sequence
• Arithmetic progressions
• Sum of the first n natural numbers
• Geometric progressions

Predicting What Comes Next: Exploring Sequences and Progressions practice questions with answers

1. Q1Multiple choice·1 mark
   What is the 10th term of the arithmetic progression $3, 7, 11, 15, \dots$?

   1. (a)39
   2. (b)37
   3. (c)41
   4. (d)35
   Show answer and step marks

   1. Correct option: (a) $39$, using $a_{10} = a + 9d = 3 + 9(4) = 39$.+1

   Answer: (a)
2. Q2Multiple choice·1 mark
   What is the sum of the first 20 natural numbers?

   1. (a)190
   2. (b)210
   3. (c)200
   4. (d)420
   Show answer and step marks

   1. Correct option: (b) $210$, using $S_n = \frac{n(n+1)}{2} = \frac{20(21)}{2} = 210$.+1

   Answer: (b)
3. Q3Multiple choice·1 mark
   The explicit rule for the nth term of the sequence $3, 7, 11, 15, \dots$ is:

   1. (a)$4n - 1$
   2. (b)$3n + 1$
   3. (c)$4n + 3$
   4. (d)$n + 4$
   Show answer and step marks

   1. Correct option: (a) $4n - 1$+1

   Answer: (a)
4. Q4Short answer·3 marks
   In an arithmetic progression, the 4th term is 14 and the 12th term is 70. Find the first term, the common difference, and the 20th term of this progression.
   Show answer and step marks

   1. Use $a_n = a + (n-1)d$: $a + 3d = 14$ and $a + 11d = 70$; subtracting gives $8d = 56 \implies d = 7$.+1
   2. Substitute to find the first term: $a + 3(7) = 14 \implies a = -7$.+1
   3. Calculate the 20th term: $a_{20} = -7 + (20-1)(7) = -7 + 133 = 126$.+1

   Answer: First term is $-7$, common difference is $7$, and the 20th term is $126$.

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