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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

In an AP, (a=\frac{7}{2}), (d=\frac{5}{2}), and (n=40). Find the sum of the first (40) terms.ExpertLevel 67In the AP (4,11,18,\ldots), what is the sum from the (25)th term to the (60)th term?ExpertLevel 67Find the sum of the AP (-25,-16,-7,\ldots,209).ExpertLevel 67Find the sum of numbers from (500) to (2000) that are divisible by (18) but not by (30).ExpertLevel 67In a saving plan, (5000) rupees are deposited in the first month and (350) rupees more every next month. What is the total deposit in (36) months?ExpertLevel 67Find the sum of all four-digit numbers divisible by (37).ExpertLevel 67Find the sum of the first (35) terms of the AP (300,287,274,\ldots).ExpertLevel 67If (S_n=3n^2+2n), find the sum from the (51)st term to the (80)th term.ExpertLevel 67In an AP, (S_{12}=540) and (S_{24}=1944). Find the value of (S_{36}).ExpertLevel 67Find the sum of the first (30) terms of the AP (250,238,226,\ldots).ExpertLevel 67What is the sum of the first 31 terms of the AP 29, 43, 57, …?ExpertLevel 67If an AP has (a=-50), (d=15), and (n=45), what is the value of (S_{45})?ExpertLevel 67In an AP, (d=11), (n=26), and (S_{26}=4290). Find the first term (a).ExpertLevel 67Find the sum of four-digit numbers that are divisible by (24) but not by (48).ExpertLevel 67Find the sum of all numbers divisible by (19) from (200) to (1200).ExpertLevel 67In an AP, (S_{10}=310) and (S_{20}=920). Find the sum from the (21)st term to the (30)th term.ExpertLevel 67If the sum of an AP is (S_n=5n^2-4n), find the (35)th term.ExpertLevel 67In an auditorium, the seats in rows are (40,48,56,\ldots). How many seats are there from the (30)th row to the (75)th row?ExpertLevel 67How many first terms of the AP (11,20,29,\ldots) have sum (3973)?ExpertLevel 67In an AP, the sum of the first and last terms is 420, and the total sum is 7350. Find the number of terms.MediumLevel 67