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 (a,b,c) are in an arithmetic progression and a=-6, c=18, what is (b-a)?In which option do the terms decrease equally but (d) is not (-9)?If the terms (5, 5+d, 5+2d) become (5, -1, -7), what is d?If (4, 9, 14,\ldots) and (20, 16, 12,\ldots) are added term by term, what type will the new sequence be?If (1, 4, 7,\ldots) is subtracted term by term from (13, 13, 13,\ldots), what will be (d) of the new sequence?If (-10, s, 2, 8) are consecutive terms of an arithmetic progression, what will (s) be?If half of each term of (2, 8, 14,\ldots) is taken and (5) is added, what will be (d) of the new sequence?If (q-3, 2q+1, 4q-1) are in an arithmetic progression, what will (q) be?Which sequence has (d=-\frac{4}{5})?If the square of its term number is added to each term of (7, 11, 15,\ldots), will the new sequence be an arithmetic progression?If (a+3d-a=27) in (a, a+d, a+2d, a+3d), what is (d)?If (2, x, 3x, 26) are consecutive terms of an arithmetic progression, what is (x)?If (2x+1, 5x-2, 8x-5) are in an arithmetic progression, which statement is correct?If the termwise sum of (16, 12, 8,\ldots) and (5, 7, 9,\ldots) is taken, what will be (d) of the new sequence?If the opposite of each term of (10, 15, 20,\ldots) is taken and (4) is added, what will be (d) of the new sequence?If (k+1, 2k+4, 4k-2) are in an arithmetic progression, what will be the value of (k)?If each term of (1, 4, 7,\ldots) is multiplied by its term number, will the new sequence be an arithmetic progression?If (4, x+2, 2x+1, 19) are in an arithmetic progression, what should be the value of (x)?An arithmetic progression has (d=-7). If every term is multiplied by (-3), what will be (d) of the new sequence?If (2m-3, 3m+1, 5m-2) are in an arithmetic progression, what will be the common difference?