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
If (5x+2, 3x+10, x+18) are in an arithmetic progression, what is the common difference?If (5) is added to each term of (10, 6, 2, -2,\ldots), what will be the common difference of the new sequence?If each term of (6, 11, 16, 21,\ldots) is multiplied by (3), what will be the new common difference?If (2, 9, 16, 23,\ldots) is written in reverse order, what will happen to the sign of the common difference?If (x+1, 2x-1, 3x-3) are in an arithmetic progression, which statement is correct?If the opposite of each term of (7, 3, -1, -5,\ldots) is taken, what will be (d) of the new sequence?Which sequence is an arithmetic progression with (d=\frac{5}{6})?If (2, x+1, 3x-1, 14) are consecutive terms of an arithmetic progression, what is (x)?What is the common difference of the sequence (0.75, 1.2, 1.65, 2.10,\ldots)?If (r-6, r-1, r+4,\ldots) is an arithmetic progression, what is (d)?If (2a, 3a+1, 5a-1) are in an arithmetic progression, what will be the value of (a)?If (2n) is subtracted from each term of (9, 13, 17,\ldots), where (n) is the term number, what will be the new common difference?In an arithmetic progression, the difference between the second and fifth terms is (18). What is (d)?In an arithmetic progression, the difference between the fourth and first terms is (-15). What is the common difference?If each term of (1, 4, 7, 10,\ldots) is increased by its term number, what will be the new (d)?Which statement is correct for the sequence (5, 5+2q, 5+4q, 5+6q,\ldots)?If each term of (11, 8, 5, 2,\ldots) is multiplied by (-2), what will be (d) of the new sequence?If (x, 2x+3, 4x+1) are in an arithmetic progression, what is the common difference?What is (d) in the sequence \(-\frac{3}{2}, -\frac{5}{6}, -\frac{1}{6}, \frac{1}{2},\ldots\)?For which (m) will (m+2, 2m+5, 4m+1) be in an arithmetic progression?