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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

If S_n = 6n² + 2n, what is a + d for this arithmetic progression?HardLevel 68What is the maximum value of the sum of initial terms of the arithmetic progression (100,94,88,\ldots)?ExpertLevel 68What is the sum of natural numbers from (1) to (150) that are not divisible by (6)?ExpertLevel 68In an arithmetic progression (S_{14}=777) and (t_{14}=96). What is the first term?ExpertLevel 68If an arithmetic progression has first term \(a\) and \(n\)th term \(l\), which is the correct formula for the sum of its first \(n\) terms?ExpertLevel 68A stair pattern has (45) bricks in the bottom row and (3) fewer bricks in each upper row. How many bricks are there in (12) rows?ExpertLevel 68If in an arithmetic progression (S_8:S_{16}=1:3) and (a=10), what is the common difference?ExpertLevel 68The sum of the first (n) terms of the arithmetic progression (2,8,14,\ldots) equals (12) times the (n)th term. What is (n)?ExpertLevel 68What is the sum of two-digit numbers that leave remainder (2) when divided by (5)?ExpertLevel 68In an arithmetic progression the sum of the first (12) terms is (420) and the sum of the next (12) terms is (1188). What is the common difference?ExpertLevel 68In the arithmetic progression (30,34,38,\ldots), what is the sum from the (6)th term to the (25)th term?ExpertLevel 68If (S_n=9n-3n^2), what is the maximum value of the sum of initial terms?ExpertLevel 68An arithmetic progression has (31) terms and the middle term is (44). What is the sum of all terms?ExpertLevel 68The sum of the first \(n\) terms of an arithmetic progression is zero, where \(n\) is a positive integer. Which of the following statements is always true?ExpertLevel 68What is the sum of numbers between (10) and (130) that are divisible by both (4) and (6)?ExpertLevel 68How many first terms of the arithmetic progression (16,23,30,\ldots) have sum (1085)?ExpertLevel 68In an arithmetic progression (S_{2n}=4S_n). If the first term is (9), what is the common difference?ExpertLevel 68In an arithmetic progression (S_{11}=385). What is the (6)th term?ExpertLevel 68In an arithmetic progression (S_{20}=740) and (S_{10}=170). What is the value of (d)?ExpertLevel 68In a school, 35 plants were planted in the first week and 8 more plants were planted each following week. How many plants will be planted in 16 weeks?MediumLevel 68