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
Find the sum of the first (17) terms of the arithmetic progression (9,15,21,\ldots).Riya saves money daily for 12 days. She saves ₹50 on the first day and ₹10 more on each successive day. She claims that her total saving is ₹2520. Which of the following analyses is correct?What is the sum of the first (16) terms of the arithmetic progression (-8,-1,6,\ldots)?Find the sum of the first (15) terms of the arithmetic progression (20,16,12,\ldots).What will be the sum of the first (21) terms of the arithmetic progression (5,14,23,\ldots)?If an arithmetic progression has first term (14), common difference (6), and (20) terms, what is the sum?Find the sum of the first (19) terms of the arithmetic progression (-12,-7,-2,\ldots).What is the sum of the first (22) terms of the arithmetic progression (3,11,19,\ldots)?What will be the sum of the first (18) terms of the arithmetic progression (25,22,19,\ldots)?Find the sum of the first (14) terms of the arithmetic progression (11,22,33,\ldots).What is the sum of the first (17) terms of the arithmetic progression (40,35,30,\ldots)?Find the sum of the first (15) terms of the arithmetic progression (7,20,33,\ldots).What is the sum of the first (23) terms of the arithmetic progression (16,20,24,\ldots)?Find the sum of the first (18) terms of the arithmetic progression (-20,-14,-8,\ldots).What will be the sum of the first (16) terms of the arithmetic progression (2,17,32,\ldots)?If the first term of an arithmetic progression is (18), the last term is (126), and there are (19) terms, what is the sum?The first term of an arithmetic progression is (9), the last term is (147), and the number of terms is (24). Find the sum.If an arithmetic progression has first term \(a\), \(n\)th (last) term \(l\), and \(n\) terms in all, which is the correct formula for the sum \(S_n\) of its first \(n\) terms?Which formula is appropriate for finding the sum of the first n terms of an arithmetic progression when the first term a and the last term l are known?If the first term of an arithmetic progression is (85), the last term is (0), and the number of terms is (18), what is the sum?