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
If an arithmetic progression has first term \(a\), common difference \(d\), and \(n\) terms, which formula correctly represents the sum of its first \(n\) terms?Find the sum of the first (15) terms of the AP (4,8,12,\ldots).Which formula correctly represents the sum of the first \(n\) terms of an AP with first term \(a\) and common difference \(d\)?What is the sum of the first (25) terms of the AP (1,3,5,\ldots)?What is the sum of the first (12) terms of the AP (10,20,30,\ldots)?What will be the sum of the first (10) terms of the AP (7,14,21,\ldots)?If the first term of an AP is (5), the last term is (45), and the number of terms is (9), what is the sum?Find the sum of the first (30) terms of the AP (3,6,9,\ldots).What is the sum of the first (8) terms of the AP (20,18,16,\ldots)?If the AP is (9,13,17,\ldots), what is the sum of the first (11) terms?What is the sum of the first (14) terms of the AP (12,17,22,\ldots)?If the sum of the first n terms of an arithmetic progression is \(S_n=3n^2+2n\), what is the first term of the progression?If an arithmetic progression has first term \(a\), common difference \(d\), and \(n\) terms, which formula correctly gives the sum \(S_n\) of its first \(n\) terms?What is the sum of the first (9) terms of the AP (6,11,16,\ldots)?If an arithmetic progression has first term \(a\), common difference \(d\), and \(n\) terms, which is the correct formula for the sum \(S_n\) of its first \(n\) terms?What is the sum of the first (16) even natural numbers?What is the sum of the first (13) terms of the AP (15,25,35,\ldots)?If the sum of the first (n) terms is \(S_n=\frac{n}{2}(3n+1)\), what is \(S_{10}\)?Find the sum of the first (10) terms of the AP (30,27,24,\ldots).Which of the following statements is correct about the formula for the sum of the first n terms of an arithmetic progression (AP)?