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 10 terms of the arithmetic progression (14, 17, 20, ...).If an arithmetic progression has first term \(a\), last term \(l\), and \(n\) terms, which is the correct formula for the sum of its first \(n\) terms?What is the sum of the first (9) terms of the arithmetic progression (50,45,40,\ldots)?If the sum of the first (6) terms of an arithmetic progression is (75), and the sum of the first (12) terms is (210), what is the sum of the (7)th to (12)th terms?What is the sum of the first (8) terms of the arithmetic progression (7,14,21,\ldots)?If the first term \(a\), last term \(l\), and total number of terms \(n\) of an arithmetic progression are known, which formula is directly used to find the sum of the first \(n\) terms?Find the sum of the first (14) terms of the arithmetic progression (2,5,8,\ldots).In a savings plan, the amount increases as (100,150,200,\ldots) rupees. What will be the total savings in the first (6) months?What will be the sum of the first (9) terms of the arithmetic progression (16,19,22,\ldots)?If \(S_n=\frac{n}{2}(a+l)\), \(a=25\), \(l=5\), and \(n=7\), what is the sum?Find the sum of the first (5) terms of the arithmetic progression (11,22,33,\ldots).The sum of the first (10) terms of an arithmetic progression is (145), and the sum of the first (5) terms is (45). What is the sum of the (6)th to (10)th terms?What is the sum of the first 7 terms of the arithmetic progression (18, 24, 30, ...)?In a staircase, the number of bricks is (3, 6, 9, ...). How many bricks will be used in the first 12 levels?If the average of the first (8) terms of an arithmetic progression is (18), what is the sum of the first (8) terms?Find the sum of the first (10) terms of the arithmetic progression (40,37,34,\ldots).If (a=1), (d=1), and (n=50), what is the sum of the first (50) terms of the arithmetic progression?What will be the sum of the first (6) terms of the arithmetic progression (21,28,35,\ldots)?Find the sum of the first (8) terms of the arithmetic progression (17,23,29,\ldots).In a library, shelves are arranged with (12,16,20,\ldots) books. How many books will there be in the first (11) shelves?