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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

What is the sum of the first (23) terms of the AP (19,30,41,\ldots)?HardLevel 69If an AP has a = -35, d = 12, and n = 28, what is the value of S₍₂₈₎?HardLevel 69In an AP, (d=9), (n=20), and (S_{20}=2450). Find the first term (a).HardLevel 69Find the sum of all three-digit numbers that are divisible by (21) but not by (42).HardLevel 69Find the sum of all numbers divisible by (16) from (120) to (900).HardLevel 69If in an AP S₂₂ = 1474 and S₁₁ = 407, what is the sum from the 12th term to the 22nd term?HardLevel 69If the sum of an AP is (S_n=4n^2+9n), find the (27)th term.HardLevel 69In an auditorium, the seats in rows are (30,36,42,\ldots). How many seats are there from the (25)th row to the (50)th row?HardLevel 69How many first terms of the AP (16,25,34,\ldots) have sum (2030)?HardLevel 69In an AP, the sum of the first and last terms is 340, and the total sum is 5780. Find the number of terms.MediumLevel 69Find the sum of all two-digit numbers that leave remainder (4) when divided by (9).HardLevel 69In the AP (-30,-22,-14,\ldots), what is the sum from the (18)th term to the (50)th term?HardLevel 69If Sₙ = 7n² − 2n, find the sum from the 41st term to the 60th term.HardLevel 69In an AP, (S_{15}=495) and (S_{30}=1890). Find the value of (S_{45}).HardLevel 69If in an AP (S_{24}=1560) and (S_{12}=456), what is the sum from the (13)th term to the (24)th term?HardLevel 69The (9)th term of an AP is (49), and the (24)th term is (124). Find the sum of the first (35) terms.HardLevel 69The first term of an AP is (5), and its (12)th term is (4) times its (3)rd term. What is the sum of the first (20) terms?HardLevel 69For the AP (7,16,25,\ldots), after how many first terms will the sum exceed (5000) for the first time?HardLevel 69The (n)th term of an AP is (a_n=5n-2). Find the sum of the first (70) terms.HardLevel 69If an arithmetic progression has first term \(a\) and common difference \(d\), which of the following expressions represents the sum \(S_n\) of its first \(n\) terms?HardLevel 69