Mathematics
Finding the sum of the first $n$ terms of an AP
समांतर श्रेणी के प्रथम n पदों का योग ज्ञात करना
In this Class 10 Mathematics topic from Arithmetic Progressions (AP), students learn how to find the sum of the first n terms of an arithmetic progression. They identify the first term, common difference, and number of terms, then apply the formulas Sₙ = n/2 [2a + (n−1)d] and Sₙ = n/2(a + l) when the last term is known. Examples help learners solve numerical problems, verify results, and understand the pattern behind sums in an AP.
Practice questions
What is the sum of the first (9) terms of the AP (11,22,33,\ldots)?What is the sum of the first (12) terms of the AP (13,16,19,\ldots)?Which is the correct formula for the sum of the first n terms of an arithmetic progression, where a is the first term and d is the common difference?What will be the sum of the first (20) terms of the AP (18,21,24,\ldots)?What is the sum of the first (7) terms of the AP (40,35,30,\ldots)?If the first term, last term, and number of terms of an arithmetic progression are known, which formula is appropriate for finding the sum of its first \(n\) terms?What is the sum of the first (50) terms of the AP (2,4,6,\ldots)?What is the sum of the first (12) terms of the AP (9,18,27,\ldots)?What is the sum of the first (6) terms of the AP (100,90,80,\ldots)?If \(S_n=\frac{n}{2}(2n+4)\), what is \(S_{12}\)?In an auditorium, the first row has 14 chairs and each successive row has 4 more chairs. If there are 9 rows in total, which conclusion is correct?The first (5) terms of an AP are (3,7,11,15,19). What is their sum?What is the sum of the first (8) terms of the AP (21,28,35,\ldots)?Which is the correct formula for the sum \(S_n\) of the first \(n\) terms of an arithmetic progression with first term \(a\) and common difference \(d\)?What is the sum of the first (9) terms of the AP (50,45,40,\ldots)?Find the sum of the first (11) terms of the AP (0,4,8,\ldots).An arithmetic progression (AP) has first term \(a\) and common difference \(d\). Which formula correctly represents the sum \(S_n\) of its first \(n\) terms?What is the sum of the first (25) terms of the AP (14,18,22,\ldots)?In an AP, the first term is (12), the last term is (72), and total terms are (11). What is the sum?What is the sum of the first (16) terms of the AP (24,30,36,\ldots)?