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
An AP has first term (8), last term (62), and number of terms (10). Find the sum of all terms.If S_n = 3n^2 + 2n, what is the sum of the first 12 terms?The numbers of seats in rows of an auditorium are (18,21,24,\ldots). How many seats are there in the first (16) rows?Find the sum of the first (18) terms of the AP (50,47,44,\ldots).If an AP has (a=4), (l=100), and (S_n=1040), what is the number of terms (n)?What is the sum of the first (40) positive even numbers?In an AP, (a=9) and (d=6). If (S_n=525), what is the value of (n)?How many initial terms of the AP (2,7,12,\ldots) have sum (287)?If (S_{10}=250) and (S_9=207), what is the (10)th term?The sum of the first (n) terms of the AP (6,11,16,\ldots) is (660). Find (n).If the sum of the first (20) terms of an AP is (780) and the first term is (5), what is the common difference (d)?In a saving plan, Ravi deposits (500) rupees in the first month and (100) rupees more each next month. What is the total deposit in (12) months?Find the sum of the first (18) terms of the AP (15,19,23,\ldots).Find the sum of all (3)-digit numbers that are divisible by (9).In an AP, (S_n=2n^2+5n). What is the sum of the first (8) terms?If an AP has (a=20), (d=-1), and (n=25), what is (S_{25})?What is the sum of the first (14) terms of the AP (4,10,16,\ldots)?A factory produces 120, 135, 150, ... items per day. What is the total production in 10 days?If an AP has first term (11), last term (71), and sum (574), what is the number of terms?Find the sum of the first (20) terms of the AP (31,28,25,\ldots).