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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 all positive multiples of (4) less than (50)?MediumLevel 69In the AP 5, 9, 13, ..., how many first terms have sum 434?HardLevel 69On a road, the distances of intervals are (6,12,18,\ldots) meters. What is the total distance of the first (25) intervals?MediumLevel 69If (S_n=5n^2-n), what is the value of (S_9)?MediumLevel 69Find the sum of the AP (7, 12, 17, ..., 82).MediumLevel 69If (a=25), (d=-4), and (S_n=105), what is the correct positive value of (n)?MediumLevel 69Find the sum of the first 32 natural numbers.EasyLevel 69What is the sum of the first 13 terms of the AP 9, 16, 23, ...?MediumLevel 69If an arithmetic progression has first term \(a\) and common difference \(d\), which is the correct formula for the sum \(S_n\) of its first \(n\) terms?MediumLevel 69In an AP, the first term is 14, the last term is 104, and the number of terms is 19. What is the sum?MediumLevel 69In an AP, (a=14), (d=7), and (n=28). Find the sum of the first (28) terms.HardLevel 67In the AP (5,9,13,\ldots), what is the sum from the (13)th term to the (30)th term?HardLevel 67Find the sum of the AP (12,18,24,\ldots,192).HardLevel 67Find the sum of all numbers divisible by (11) between (100) and (500).HardLevel 67In a saving plan, (1500) rupees are deposited in the first month and (250) rupees more every next month. What is the total deposit in (18) months?HardLevel 67Find the sum of all three-digit numbers that are divisible by (13).HardLevel 67In the AP (50, 47, 44, ...), what is the sum of the terms from the 6th term to the 20th term, inclusive?HardLevel 67If the sum of the first n terms of an AP is Sₙ = 4n² − 3n, find the sum of the terms from the 12th term to the 20th term, inclusive.HardLevel 67In an AP, (S_{10}=250) and (S_{20}=900). Find the value of (S_{30}).HardLevel 67Find the sum of the first (18) terms of the AP (80,75,70,\ldots).HardLevel 67