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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

Find the sum of the first (6) terms of the arithmetic progression (16,32,48,\ldots).EasyLevel 69 If the sum of the first (10) terms of an arithmetic progression is (310), and the last term is (49), what is the first term?EasyLevel 69 What is the sum of the first (10) terms of the arithmetic progression (75,70,65,\ldots)?EasyLevel 69 In a shop, packets are arranged in the numbers (7,14,21,\ldots). How many packets will there be in the first (9) shelves?EasyLevel 69 What is the sum of the first 16 odd natural numbers?EasyLevel 69 If (a=9), (d=9), and (n=8), what will be the sum of the first (8) terms of the arithmetic progression?EasyLevel 69 Find the sum of the first (14) terms of the arithmetic progression (22,25,28,\ldots).EasyLevel 69 In an arithmetic progression, the first term is (31), the last term is (13), and the number of terms is (7). What is the sum?EasyLevel 69 What will be the sum of the first (35) natural numbers?EasyLevel 69 What will be the sum of the first (12) terms of the arithmetic progression (10,18,26,\ldots)?EasyLevel 69 Find the sum of the first (18) terms of the arithmetic progression (7,12,17,\ldots).MediumLevel 67 If an arithmetic progression has a = 3, d = 7, and n = 20, what is the sum of the first 20 terms?MediumLevel 67 What is the sum of the first (15) terms of the arithmetic progression (-5,-1,3,\ldots)?MediumLevel 67 If the first term of an arithmetic progression is (11), the last term is (83), and there are (13) terms, what is the sum?MediumLevel 67 Find the sum of the first (14) terms of the arithmetic progression (60,55,50,\ldots).MediumLevel 67 If an arithmetic progression has S₁₀ = 270 and S₅ = 85, what is the sum of the 6th to 10th terms?EasyLevel 67 The (n)th term of an arithmetic progression is (a_n=4n-1). Find the sum of the first (12) terms.MediumLevel 67 In a theatre, rows of seats follow (18,22,26,\ldots). How many seats will there be in the first (16) rows?MediumLevel 67 What will be the sum of the first (17) terms of an arithmetic progression starting with (5) and having common difference (9)?MediumLevel 67 If the sum of the first (n) natural numbers is (325), what is the value of (n)?MediumLevel 67