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
If an arithmetic progression has S₇ = 126 and S₁₄ = 427, what is the sum of the 8th to 14th terms?What is the sum of the multiples of (4) from (4) to (100)?What is the sum of the first 18 terms of the arithmetic progression 13, 17, 21, …?If the sum of the first (n) odd natural numbers is (441), what is the value of (n)?The average of the first (11) terms of an arithmetic progression is (42). What will be the sum of these (11) terms?If an arithmetic progression has (a=16), (d=6), and (S_n=640), what is the value of (n)?Find the sum of the first (19) terms of the arithmetic progression (4,14,24,\ldots).If (S_n=2n^2+5n) for an arithmetic progression, what will be the sum of the first (15) terms?In the arithmetic progression (6,15,24,\ldots), the sum of how many first terms will be (1035)?Find the sum of the numbers divisible by (8) between (100) and (250).If an arithmetic progression has (S_6=111) and (S_{13}=494), what is the sum of the (7)th to (13)th terms?What will be the sum of the first (15) terms of the arithmetic progression (72,66,60,\ldots)?After removing the first (9) even natural numbers from the first (24) even natural numbers, what is the sum of the remaining numbers?Find the sum of the first (14) terms of the arithmetic progression (10,21,32,\ldots).The sum of the first n terms of a sequence is \(S_n\), with \(S_0=0\). Which of the following conditions is necessary and sufficient to prove that the sequence is an arithmetic progression?In the arithmetic progression (8,14,20,\ldots), the sum of how many first terms will be (750)?Find the sum of the numbers divisible by (12) between (200) and (400).If an arithmetic progression has (S_9=225) and (S_{18}=855), what is the sum of the (10)th to (18)th terms?What will be the sum of the first (13) terms of the arithmetic progression (96,88,80,\ldots)?In a construction work, rows of bricks follow (24,31,38,\ldots). How many bricks will be used in the first (18) rows?