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 the first (13) terms of the arithmetic progression (2,9,16,\ldots)?If an arithmetic progression has (S_5=65) and (S_{11}=242), what is the sum of the (6)th to (11)th terms?Find the sum of the first (17) even natural numbers.What is the sum of the first (7) terms of the arithmetic progression (60,55,50,\ldots)?The sum of the first (6) terms of an arithmetic progression is (126). If the average of the first (6) terms is asked, what will it be?Find the sum of the first (16) terms of the arithmetic progression (13,18,23,\ldots).In a staircase, the number of bricks increases as (5,10,15,\ldots). How many bricks will be used in the first (9) levels?If the first term of an arithmetic progression is (11), the last term is (71), and the number of terms is (16), what is the sum?What is the sum of the first (11) terms of the arithmetic progression (8,16,24,\ldots)?Find the sum of the first (28) natural numbers.What will be the sum of the first (6) terms of the arithmetic progression (90,84,78,\ldots)?Which formula correctly represents the sum of the first n terms of an arithmetic progression, where the first term is a and the common difference is d?In a plantation campaign, plants are planted in the pattern (6,11,16,\ldots). How many plants will be planted in the first (10) days?What is the sum of the first (18) terms of the arithmetic progression (1,6,11,\ldots)?If \(S_n=\frac{n}{2}(a+l)\), \(a=14\), \(l=84\), and \(n=15\), find the sum.What is the sum of the first (21) even natural numbers?Find the sum of the first (12) terms of the arithmetic progression (17,20,23,\ldots).The sum of the first (9) terms of an arithmetic progression is (198). What will be the average of the first (9) terms?What will be the sum of the first (7) terms of the arithmetic progression (5,13,21,\ldots)?If an arithmetic progression has (S_4=44) and (S_9=189), what is the sum of the (5)th to (9)th terms?