Mathematics
Introduction to APs and common difference.
समांतर श्रेणियों (AP) और सार्व अंतर का परिचय
In this Class 10 Mathematics topic from Arithmetic Progressions (AP), students learn what an arithmetic progression is and how to recognize its pattern. They explore the first term, the common difference, and the role of a constant change between consecutive terms. The topic also develops skills for writing the general form of an AP, finding missing terms, and deciding whether a given sequence follows an arithmetic pattern through examples and simple reasoning.
Practice questions
In the sequence (0,-4,-8,-12,\ldots), what are (a) and (d) respectively?In a training program, running distance increases by (0.4) km each day. The distances are (1.2,1.6,2.0,2.4,\ldots). What is the difference between the third and first terms?If (3) is added to each term of (10,16,22,28,\ldots), what will be (d) of the new sequence?If the first two terms of an arithmetic progression are (-12) and (-7), what will be the third term?What is the common difference in the sequence (3a,3a-4,3a-8,\ldots)?If 13, b, 31 are consecutive terms of an arithmetic progression, what is b?Which sequence has (d=\frac{3}{4})?If (a=5) and the second term is (17), what is (d)?What is (d) in the sequence (2.2,3.1,4.0,4.9,\ldots)?If (d) is to be found in (28,21,14,7,\ldots), which calculation is correct?In an arithmetic progression, (d=9) and the second term is (20). What is the first term?If each term of the arithmetic progression (3,8,13,18,\ldots) is multiplied by (2), what will be the common difference of the new sequence?If the sequence (6,12,18,24,\ldots) is written in reverse order, what will be (d) of the new sequence?If (5,x,y,20) are consecutive terms of an arithmetic progression, what will be the values of (x) and (y)?If (2x-3, x+4, 3x-1) are consecutive terms of an arithmetic progression, what is the value of (x)?If (a-2, 2a+1, 5a-4) are in an arithmetic progression, what is the common difference?When will the sequence (7, 7+p, 7+3p, 7+6p,\ldots) be an arithmetic progression?If (4, y, 16, 22) are consecutive terms of an arithmetic progression, what will be the value of (y)?If (3, x, y, 24) are consecutive terms of an arithmetic progression, what is the value of (x+y)?What is the common difference of the sequence (\frac{2}{5}, \frac{7}{10}, 1, \frac{13}{10},\ldots)?