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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

The (12)th term of an AP is (41), and the (25)th term is (80). Find the sum of the first (50) terms.In the AP (12,17,22,\ldots), find the sum from the (21)st term to the (40)th term.In an AP, the sum of the first 15 terms equals the sum of the first 21 terms, i.e., \(S_{15}=S_{21}\). If the first term is \(a\) and the common difference is \(d\), which of the following relation must be true?In an AP, a = 3 and the sum from the 11th term to the 20th term is 465. Find d.If in an AP (S_5=75) and (S_{15}=525), find the value of (S_{25}).Find the sum of all numbers from (1) to (500) that are divisible by (3) or (5).Find the sum of all two-digit numbers that leave remainder (2) when divided by (7).The (6)th term of an AP is (31), and the sum of the first (6) terms is (111). Find the sum of the first (12) terms.In an AP, (a=2), and (S_{15}=6S_5). What is the common difference (d)?The first term of an AP is (x), and the common difference is (x+2). If the sum of the first (10) terms is (365), what is the value of (x)?Find the sum of all numbers from (200) to (500) that are divisible by (8) but not by (16).If in an AP, S₅ = 75 and S₁₀ = 275, what is the value of S₂₀?Find the sum of all numbers from (1) to (1000) that are divisible by (4) but not by (10).If the sum of an AP is (S_n=7n^2-4n), find the sum from the (21)st term to the (30)th term.In an AP, the sum of the first (20) terms is (740), and the (20)th term is (60). Find the first term.In an AP, (a=17), (d=8), and (n=24). Find the sum of the first (24) terms.In the AP (3,10,17,\ldots), what is the sum from the (15)th term to the (32)nd term?Find the sum of the AP (-6,1,8,\ldots,169).Find the sum of all numbers divisible by (14) from (200) to (800).In a saving plan, (2200) rupees are deposited in the first month and (175) rupees more every next month. What is the total deposit in (24) months?