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
Which of the following explicit rules represents an arithmetic progression (AP)?Which explicit rule is correct for the sequence (7,14,21,28,\ldots)?If (a_n=2n+5), what are (a_1) and (a_2)?What is the general term of the sequence (12, 15, 18, 21, …)?The general term of a sequence is \(a_n=4n+3\). Which statement about this sequence is correct?What is the general term of the sequence (1, 4, 9, 16, …)?If (a_n=n^2+1), what is the value of (a_4)?Which general term is correct for the sequence (2,5,10,17,\ldots)?What is the general term of the sequence (9,8,7,6,\ldots)?If (a_n=15-2n), what is the value of (a_5)?Which explicit rule is correct for the sequence (13,11,9,7,\ldots)?If (a_n=2^n), what is the value of (a_3)?What is the general term of the sequence (2,4,8,16,\ldots)?If (a_n=3^n), what is the value of (a_2)?Which general term is correct for the sequence (3,9,27,81,\ldots)?If (a_n=n^2-n), what is the value of (a_5)?What is the general term of the sequence (0,2,6,12,\ldots)?A sequence has the general term \(a_n=7\). What type of sequence is it?Which rule is correct for the sequence (7, 11, 15, 19, …)?Which statement is correct about the sequence whose general term is \(a_n=5n+2\)?