Mathematics
Sequences
अनुक्रम
In this Class 9 Mathematics topic from Sequences and Progressions, students learn how numbers or objects are arranged in a definite order and how to identify the rule connecting successive terms. They practise finding missing terms, writing a sequence from a given pattern, and expressing its general term when the relationship is clear. The topic develops pattern recognition, logical reasoning, and accuracy, while preparing students to understand progressions and solve sequence-based problems in later mathematics.
Practice questions
If (a_n=\frac{n(n+3)}{2}), which term is (65)?In the sequence (2,5,9,16,28,\ldots), the differences of differences are (1,3,5,\ldots). What will be the next term?What will be the 10th term in the sequence (1, 4, 2, 8, 3, 16, 4, ...)?Which of the following sequences has non-constant consecutive first differences but constant second differences?In the sequence (2,7,17,32,52,\ldots), the successive differences are (5,10,15,20,\ldots). What will be the next term?In the sequence (120, 117, 111, 102, 90, ...), the differences are (-3, -6, -9, -12, ...). What will be the next term?In the sequence (4,9,8,18,16,36,\ldots), two different patterns are hidden. What will be the next term?If (a_1=2) and (a_{n+1}=3a_n-1), what will be the value of (a_5)?If (a_1=1) and (a_{n+1}=a_n+n(n+1)), what will (a_5) be?What will be the (12)th term in the sequence (\frac{2}{3},\frac{3}{5},\frac{4}{7},\ldots)?If (a_n=2^n-n), what will be the value of (a_8)?If (a_n=2n^2+3n), how many terms will be less than (300)?In the sequence (5,12,x,50,85), the successive differences are (7,15,23,35). What is the value of (x)?In the sequence 200, 188, 171, x, 122, the differences are -12, -17, -22, -27. What will x be?In the sequence (2,6,14,30,62,\ldots), each next term is obtained by doubling the previous term and adding (2). What will be the next term?In the sequence (2,4,12,48,240,\ldots), the multiplier pattern is (2,3,4,5,\ldots). What will be the next term?What is the sum of the first 6 terms of the sequence (2, 5, 10, 17, 26, …)?Which of the following sequences is an arithmetic progression, that is, the difference between each term and its immediately preceding term remains constant?Which of the following sequences has non-constant first differences but constant second differences between consecutive terms?In the sequence (\frac{1}{3},\frac{1}{6},\frac{1}{9},\ldots), which is the first term less than (\frac{1}{50})?