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
For which (r) will (9, 9+r, 9+4r, 9+9r,\ldots) be an arithmetic progression?If (18, 14, 10, 6,\ldots) is viewed in reverse order, what will be the common difference?If (1, 6, 11,\ldots) and (4, 7, 10,\ldots) are added term by term, what will be (d) of the formed sequence?If (2, 7, 12,\ldots) is subtracted term by term from (30, 24, 18,\ldots), what will be the common difference of the new sequence?What is the common difference in the sequence \(-\frac{7}{4}, -1, -\frac{1}{4}, \frac{1}{2},\ldots\)?If (0.8, 1.35, 1.90, 2.45,\ldots) is an arithmetic progression, what is (d)?If (u-8, u-2, u+4,\ldots) is an arithmetic progression, what is (d)?In an arithmetic progression, the difference between the third and seventh terms is (28). What is the common difference?In an arithmetic progression, the difference between the fifth and second terms is (-18). What will (d) be?If (2,4,6) are added respectively to (a,a+d,a+2d), what will be the new common difference?If the term number (n) is subtracted from each term of (8, 14, 20,\ldots), what will be the new (d)?Which sequence is not an arithmetic progression even though the first two differences are equal?If (x-7, x-1, x+5) are in an arithmetic progression, what is the correct statement about (x)?If (2x, x+9, 18) are in an arithmetic progression, what will be the value of (x)?If each term of (5, 11, 17,\ldots) is multiplied by (-\frac{1}{3}), what will be (d) of the new sequence?If a new sequence (3^2, 7^2, 11^2,\ldots) is formed from (3, 7, 11,\ldots), what type will the new sequence be?If the fourth term of (7, 7+d, 7+2d, 7+3d) is 34, what is the second term?Which sequence is an arithmetic progression with (a=15) and (d=-\frac{5}{2})?If (3v-4, 4v+1, 6v-1) are in an arithmetic progression, what is the value of (v)?If (4n) is subtracted from each term of (2, 5, 8,\ldots), where (n) is the term number, what will be the new common difference?