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 (x) do the terms (2x+3,5x-1,8x-5) form an AP?What is the common difference of (\frac{2}{3},\frac{1}{6},-\frac{1}{3},-\frac{5}{6},\ldots)?Is the sequence (a_n=\frac{n+1}{n}) an AP?A finite AP (a,a+d,a+2d,a+3d) is reversed as (a+3d,a+2d,a+d,a). What is the common difference of the new order?What is the common difference of the sequence (a_n=9-5n)?Is the sequence (1,8,27,64,\ldots) an AP?If (4t+1,t+10,-t+21) are consecutive terms of an AP, what are (t) and (d)?The consecutive AP terms are (-17,z,23). What are (z) and the common difference?What is the common difference of (2p − q, 2p + 2q, 2p + 5q, 2p + 8q, …)?If a sequence has (a_{n+1}-a_n=2n+1), when will it be an AP?What is the common difference of (a_n=\frac{5n-3}{4})?In an AP, (a_4=12) and (a_{10}=-6). What is the common difference?If (x+1,2x+6,5x-2) are consecutive terms of an AP, what are (x) and (d)?Which sequence is an AP with common difference (0.75)?The temperatures form the sequence (42^\circ,38.5^\circ,35^\circ,31.5^\circ). What is the common difference?If (a_n=c-(n-1)r), what are the first term and common difference?Which statement is correct for (\sqrt{3},\sqrt{12},\sqrt{27},\sqrt{48})?If (p,q,r,s) are four consecutive terms of an AP, which relation is always true?Which condition correctly checks whether (a,b,c) are in AP?Which option gives the first four terms of an AP with (a_1=11) and (d=-2)?