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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

For the arithmetic progression (4,9,14,\ldots), after how many first terms will the sum exceed (1500) for the first time?ExpertLevel 69 In an arithmetic progression (t_{15}=65) and (S_{15}=555). What is the common difference?ExpertLevel 69 In an arithmetic progression (a=7) and (S_5:S_{15}=1:7). What is the common difference?ExpertLevel 69 The sums of the first (n) terms of the arithmetic progressions (10,14,18,\ldots) and (22,24,26,\ldots) are equal. What is the positive value of (n)?ExpertLevel 69 If (S_n=3n^2+4n) for an arithmetic progression, what is the sum from the (16)th to the (25)th terms?ExpertLevel 69 In an arithmetic progression (S_{18}=999) and (d=5). What is the first term?ExpertLevel 69 What is the maximum value of the sum of initial terms of the arithmetic progression (90,84,78,\ldots)?ExpertLevel 69 In the arithmetic progression (7,14,21,\ldots), if (S_n) is (15) times the (n)th term, what is (n)?ExpertLevel 69 What is the sum of two-digit numbers that leave remainder (4) when divided by (6)?ExpertLevel 69 The first term of an arithmetic progression is (96) and the sum of the first (25) terms is (0). What is the common difference?ExpertLevel 69 (19) arithmetic means are inserted between (6) and (126). What is the sum of the complete arithmetic progression formed?ExpertLevel 69 An arithmetic progression has (29) terms and its middle term is (48). What is the sum of all terms?ExpertLevel 69 In an arithmetic progression the first term is (6) and (S_{12}=4S_6). What is the common difference?ExpertLevel 69 If (S_n=10n-2n^2) for an arithmetic progression, what is the maximum value of the sum of initial terms?ExpertLevel 69 What is the sum of the first (60) positive odd numbers?ExpertLevel 69 How many first terms of the arithmetic progression (21,27,33,\ldots) have sum (1425)?ExpertLevel 69 What is the sum of the first 18 terms of the arithmetic progression −12, −5, 2, …?ExpertLevel 69 In an arithmetic progression (S_{10}=345) and (S_{20}=1390). What is (S_{30})?ExpertLevel 69 In an arithmetic progression the sum of the first (15) terms is (600) and the sum of the next (15) terms is (1500). What is the common difference?ExpertLevel 69 In the arithmetic progression (80,76,72,\ldots), what is the sum from the (5)th term to the (20)th term?ExpertLevel 69