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_n) has common difference (-9) and (b_n=\frac{a_n}{3}+5), what is the common difference of (b_n)?An AP has common difference (4). What is the common difference of the new sequence (a_2,a_5,a_8,\ldots)?A finite AP has common difference (-6). What will be the new common difference after writing it in reverse order?For nonzero (r), (r,r^2,r^3) form an AP. What is the value of (r)?If (\alpha,\beta,\gamma) are in AP and (\alpha+\gamma=14), what is (\beta)?If (a_n=mn+n), what is the common difference of the sequence?Which statement is correct about (1,3,6,10,15,\ldots)?What is the common difference of (\frac{7}{8},\frac{5}{8},\frac{3}{8},\frac{1}{8},\ldots)?For valid (x), can (\frac{1}{x-2},\frac{1}{x},\frac{1}{x+2}) form an AP?Which statement is correct for the three terms (a − 2b, a + b, a + 4b)?Is the sequence (2,6,18,54,\ldots) an AP?The first two terms of an AP are (\lambda-4) and (3\lambda+2). What is the common difference?Is the sequence (a_n=2n+(-1)^n) an AP?What is the common difference of (x, x + √5, x + 2√5, x + 3√5)?A vehicle covers (18,30,42,54) kilometres in equal time intervals. What is the common difference of the distance sequence?For which (k) are (k,2k+1,5k-2,8k-5) four consecutive terms of an AP?If (a_n=4n+7) and (c_n=a_{n+1}-a_n), what is the common difference of the sequence (c_n)?The numbers 14, m, and 50 are consecutive terms of an arithmetic progression (AP). What are m and d?Which information does not guarantee that an entire sequence is an AP?What is the common difference of the AP 81, 72, 63, 54, ...?