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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

Find the sum of all three-digit numbers divisible by (17).Find the sum of the first (25) terms of the AP (120,113,106,\ldots).If (S_n=5n^2-2n), find the sum from the (26)th term to the (40)th term.In an AP, (S_{12}=438) and (S_{24}=1596). Find the value of (S_{36}).Find the sum of the first 20 terms of the AP (95, 89, 83, ...).What is the sum of the first (17) terms of the AP (14,23,32,\ldots)?If an AP has a = −20, d = 9, and n = 30, what is the value of S₃₀?In an AP, (d=6), (n=18), and (S_{18}=1512). Find the first term (a).Find the sum of all three-digit numbers that are divisible by (15) but not by (30).Find the sum of all numbers divisible by (13) from (80) to (600).If in an AP (S_{18}=810) and (S_9=270), what is the sum from the (10)th term to the (18)th term?If the sum of an AP is (S_n=3n^2+5n), find the (22)nd term.In an auditorium, the seats in rows are (25,30,35,\ldots). How many seats are there from the (18)th row to the (42)nd row?How many first terms of the AP (11,18,25,\ldots) have sum (1701)?In an AP, the sum of the first and last terms is 260, and the total sum is 4160. Find the number of terms.Find the sum of all two-digit numbers that leave remainder (3) when divided by (8).In the AP (-4,2,8,\ldots), what is the sum from the (20)th term to the (45)th term?If (S_n=4n^2+n), find the sum from the (31)st term to the (45)th term.In an AP, (S_{10}=265) and (S_{20}=1030). Find the value of (S_{30}).If in an AP, S₁₆ = 880 and S₈ = 280, what is the sum from the 9th term to the 16th term?