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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

The sum of the first (12) terms is (456), and the first term is (8). If the last term is (l), what is (l)?MediumLevel 67In the arithmetic progression (2,11,20,\ldots), the sum of how many first terms will be (645)?MediumLevel 67Find the sum of all positive multiples of (6) less than (100).MediumLevel 67What is the sum of the numbers divisible by (7) between (50) and (150)?MediumLevel 67If the sum of the first (9) terms of an arithmetic progression is (279), and the first term is (7), what is the last term?MediumLevel 67What is the sum of the first (11) terms of the arithmetic progression (32,28,24,\ldots)?MediumLevel 67Fruits plucked from a tree each day were (12,18,24,\ldots). How many fruits were plucked in the first (15) days?MediumLevel 67If an arithmetic progression has (S_8=184) and (S_{15}=555), what is the sum of the (9)th to (15)th terms?MediumLevel 67After removing the first (10) odd natural numbers from the first (18) odd natural numbers, what is the sum of the remaining (8) numbers?MediumLevel 67If the first term \(a\), the last (\(n\)th) term \(l\), and the number of terms \(n\) of an arithmetic progression are known, which is the correct formula for the sum of its first \(n\) terms?MediumLevel 67In the arithmetic progression (1,8,15,\ldots), the sum of how many first terms will be (504)?MediumLevel 67In a savings plan, the deposits are (150,225,300,\ldots) rupees. What is the total saving in the first (10) months?MediumLevel 67What is the sum of the multiples of (10) from (20) to (200)?MediumLevel 67If the sum of the first n even natural numbers is 420, what is the value of n?EasyLevel 67What is the sum of the first (12) terms of the arithmetic progression (45,39,33,\ldots)?MediumLevel 67If (S_n=3n^2+2n), what will be the sum of the first (8) terms?MediumLevel 67The sum of the first (7) terms of an arithmetic progression is (203). If the first term is (5), what is the seventh term?MediumLevel 67Find the sum of the first (21) terms of the arithmetic progression (9,16,23,\ldots).MediumLevel 67If an arithmetic progression has first term (25), common difference (-2), and (16) terms, what is the sum of the first (16) terms?MediumLevel 67In a library, new books arrive each week in numbers (30,45,60,\ldots). How many books will arrive in the first (12) weeks?MediumLevel 67

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