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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 S₁₅ = 465 and S₁₀ = 240 for an AP, what is the sum from the 11th term to the 15th term, inclusive?If the sum of an AP is (S_n=2n^2+7n), find the (18)th term.In an auditorium, the seats in rows are (20,24,28,\ldots). How many seats are there from the (15)th row to the (35)th row?How many first terms of the AP (7,12,17,\ldots) have sum (1090)?In an AP, the sum of the first and last terms is 150 and the total sum is 1800. Find the number of terms.Find the sum of all two-digit numbers that leave remainder (1) when divided by (5).In the AP (6,10,14,\ldots), what is the sum from the (4)th term to the (25)th term?If Sₙ = 3n² + 4n, find the sum of the 21st term through the 30th term.In an AP, (S_8=180) and (S_{16}=680). Find the sum from the (17)th term to the (24)th term.If S₁₂ = 420 and S₆ = 150 for an AP, what is the sum from the 7th term to the 12th term, inclusive?The (5)th term of an AP is (22), and the (15)th term is (62). Find the sum of the first (20) terms.The first term of an AP is 4, and its 8th term is 3 times its 3rd term. What is the sum of the first 12 terms?For the AP (2,9,16,\ldots), after how many first terms will the sum exceed (1000) for the first time?The (n)th term of an AP is (a_n=4n-1). Find the sum of the first (50) terms.The average of the first (30) terms of an AP is (76). What is the value of (S_{30})?If in an AP (S_{10}=210) and the (10)th term is (39), find (S_{20}).If (S_n=n(5n-2)), find the sum from the (16)th term to the (25)th term.In the first (30) terms of the AP (2,5,8,\ldots), find the sum of the terms whose positions are multiples of (3).Find the sum of all two-digit numbers that are not divisible by (4).Find the sum of all three-digit numbers that are divisible by (6) but not by (12).