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
In an AP, (a_3-a_1=14). What is the common difference?In an AP, (a_2+a_4=30) and (a_3=15). What is certain about the common difference?Which statement directly confirms that a sequence is an AP?Which option is correct for the sequence (5,5,5,5,\ldots)?For valid (x), can (\frac{1}{x},\frac{1}{x+1},\frac{1}{x+2}) form an AP?If (a_n=\alpha n+\beta), what will be the common difference of the sequence?If (a,b,c,e) are four consecutive terms of an AP, which relation is always true?The consecutive AP terms are (-11,y,5). What are (y) and the common difference?Which option shows a decreasing AP?Can (3q+2,q-4,-q+10) be consecutive terms of an AP for some (q)?Is the sequence (a_n=(-1)^n n) an AP?What are the first term and common difference of aₙ = 12 − 7(n − 1)?In which sequence are the first term and the common difference equal?What is the common difference of (0.2, 0.02, −0.16, −0.34, …)?If (a_n) is an AP with common difference (4) and (b_n=2a_n-3), what is the common difference of (b_n)?If (x,y,z) are in AP and (r) is added to each, what is the common difference of the new three terms?An AP has common difference (d). If every term is multiplied by (-3), what is the new common difference?If an AP has common difference (7) and (12) is subtracted from every term, what is the new common difference?If a, b, c are in AP and a + b + c = 27, what is the middle term b?Which statement is correct for the three terms (u-v,u,u+v)?