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 the first (20) terms of the arithmetic progression (3,7,11,\ldots).The number of chairs in rows increases as (8,11,14,\ldots). How many chairs will there be in the first (10) rows?If an arithmetic progression has (S_5=50) and (S_{10}=175), what is the sum of the (6)th to (10)th terms?What will be the sum of the first (6) terms of the arithmetic progression (20,18,16,\ldots)?If S_n = n/2[2a + (n - 1)d], a = 9, d = 1, and n = 14, what is the value of S_n?What will be the sum of the first (11) terms of the arithmetic progression (1,4,7,\ldots)?The average of the first (9) terms of an arithmetic progression is (25). What is the sum of these (9) terms?The first term of an arithmetic progression is (15), the last term is (51), and the number of terms is (13). Find the sum.What is the sum of the first (5) terms of the arithmetic progression (30,25,20,\ldots)?A student solves (5,7,9,\ldots) questions per day. How many questions does he solve in the first (12) days?If the (n)th term of an arithmetic progression is (a_n=2n+1), what is the sum of the first (6) terms?Find the sum of the first (16) terms of the arithmetic progression (4,9,14,\ldots).The sum of the first (7) terms of an arithmetic progression is (140), and the first term is (5). Using the sum formula, what is the last term (l)?What is the sum of the first (10) terms of the arithmetic progression (6,12,18,\ldots)?What is the sum of the first (30) natural numbers?Find the sum of the first 15 terms of the arithmetic progression (9, 13, 17, ...).In a garden, rows of plants follow (4,8,12,\ldots). How many plants are there in the first (9) rows?If an arithmetic progression has first term 2, last term 50, and 13 terms, what is its sum?What will be the sum of the first (8) terms of the arithmetic progression (100,90,80,\ldots)?What is the sum of the first (12) odd natural numbers?