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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 all two-digit numbers that leave remainder (3) when divided by (8).HardLevel 68In the AP (-4,2,8,\ldots), what is the sum from the (20)th term to the (45)th term?HardLevel 68If (S_n=4n^2+n), find the sum from the (31)st term to the (45)th term.HardLevel 68In an AP, (S_{10}=265) and (S_{20}=1030). Find the value of (S_{30}).HardLevel 68If in an AP, S₁₆ = 880 and S₈ = 280, what is the sum from the 9th term to the 16th term?MediumLevel 68The (8)th term of an AP is (37), and the (22)nd term is (107). Find the sum of the first (30) terms.HardLevel 68The first term of an AP is (6), and its (9)th term is (2) times its (4)th term. What is the sum of the first (25) terms?HardLevel 68For the AP (4,13,22,\ldots), after how many first terms will the sum exceed (3000) for the first time?HardLevel 68The (n)th term of an AP is (a_n=6n+5). Find the sum of the first (60) terms.HardLevel 68If the sum of the first \(n\) terms of an AP is zero and \(n\) is odd, which of the following statements must be true?HardLevel 68If in an AP (S_{15}=600) and the (15)th term is (68), find (S_{30}).HardLevel 68If (S_n=n(4n+3)), find the sum from the (21)st term to the (35)th term.HardLevel 68In the first (40) terms of the AP (1,6,11,\ldots), find the sum of the terms whose positions are multiples of (4).HardLevel 68Find the sum of all three-digit numbers that are not divisible by (9).HardLevel 68Find the sum of all numbers from (100) to (900) that are divisible by (8) but not by (24).HardLevel 68The (14)th term of an AP is (52), and the (31)st term is (120). Find the sum of the first (40) terms.HardLevel 68In the AP (18,25,32,\ldots), find the sum from the (30)th term to the (55)th term.HardLevel 68In an AP, d = −9 and S₃₁ = 0. What is the first term a?HardLevel 68In an AP, a = 5, and the sum from the 16th term to the 30th term is 1395. Find d.HardLevel 68If in an AP (S_7=91) and (S_{21}=714), find the value of (S_{35}).HardLevel 68