Mathematics
Explicit or general rule
स्पष्ट या सामान्य नियम
In Class 9 Mathematics, this topic in Sequences and Progressions introduces ways to describe a sequence with a rule that works for every term. Students learn to identify patterns, express the nth term using a variable, and use an explicit or general rule to calculate terms without listing all the preceding ones. They also practise checking a rule against known terms and interpreting how a sequence changes, building a foundation for arithmetic patterns and progression problems.
Practice questions
What is the general term of the sequence (9,27,81,243,\ldots)?If (a_n=n^2+3n), what is the value of (a_4)?Which general term is correct for the sequence (4, 10, 18, 28, …)?Which statement is correct about the sequence whose general term is \(a_n=5n-2\)?What is the general term of the sequence (54,48,42,36,\ldots)?If (a_n=7n-8), which term will be equal to (41)?In the sequence (-1,6,13,20,\ldots), which term is (41)?If \(a_n=\frac{2n+1}{3}\), what is the value of \(a_4\)?What is the general term of the sequence (1,\frac{5}{3},\frac{7}{3},3,\ldots)?Which of the following explicit rules represents an arithmetic sequence in which each term is 4 greater than the preceding term?Which general term is correct for the sequence (15,26,37,48,\ldots)?Which of the following sequences has a general term in linear form, so that the difference between consecutive terms remains constant?What is the general term of the sequence (5,16,33,56,\ldots)?If (a_n=2^n+3), what is the value of (a_4)?Which explicit rule is correct for the sequence (5,7,11,19,\ldots)?If (a_n=n^2-3n), what is the value of (a_7)?What is the general term of the sequence (−2, −2, 0, 4, …)?If (a_n=25+n), what is the value of (a_6)?What is the general term of the sequence (4,9,14,19,\ldots)?Which of the following general terms represents an arithmetic progression?