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 (4, h, 20) are in an arithmetic progression and (h) is the middle term, what is (h-4)?If three times the term number is subtracted from each term of (2, 6, 10,\ldots), what will be the new common difference?For which value of k will (k−3, k+2, 2k+1) be in an arithmetic progression?For what value of (k) will (3k-2, 5k+1, 8k-3) be in an arithmetic progression?If (a, a+2d, a+5d) are in an arithmetic progression and (d \neq 0), which statement is correct?The sequence (7, x, 23, y, 39) is an arithmetic progression. What is the value of (x+y)?If (p-4, 2p+1, 4p-2) are in an arithmetic progression, what will be the common difference?The sequence (m+1, 3m−2, 6m−8) is stated not to be an arithmetic progression. For which value of m will this statement become false?If (4, r, s, 31) are in an arithmetic progression, what is the value of s−r?For which (q) will (q^2, q^2+q, q^2+3q-2) be in an arithmetic progression?A student claims that the sequence 4, 9, 14, 20 is an arithmetic progression because its terms are increasing. What is the student’s error?If (2a+3, 5a-1, 11a-13) are in an arithmetic progression, what is the second term?The sequence (18, 18-c, 18-3c) is an arithmetic progression. What is the correct conclusion about (c)?If (5, 5+t, 5+3t, 5+6t) is an arithmetic progression, which value of (t) is possible?Which condition is necessary and sufficient for four numbers \,p, q, r, s\, in this order to be consecutive terms of an arithmetic progression?If (12, b, 2b-3, 39) are in an arithmetic progression, what is the value of (b)?For what value will the common differences of (2x+5, 4x+1, 7x-7) be equal?If terms are defined by A_n=4n−9, what does A_15−A_14 represent?Which sequence has a negative common difference and all consecutive differences equal?If the terms of an arithmetic progression are (a, a+d, a+2d) and (a+d=0), what is the sum of the first and third terms?