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
The (12)th term of an AP is (64), and the (32)nd term is (184). Find the sum of the first (45) terms.The first term of an AP is (6), and its (14)th term is (3) times its (4)th term. What is the sum of the first (30) terms?For the AP (12,23,34,\ldots), after how many first terms will the sum exceed (10000) for the first time?The (n)th term of an AP is (a_n=7n-4). Find the sum of the first (80) terms.In an arithmetic progression the first term is (7) and the common difference is (5). If the sum of the first (n) terms is (1470) then what is (n)?The (8)th term of an arithmetic progression is (31) and the (20)th term is (79). What is the sum of the first (20) terms?If the sum of the first (n) terms of an arithmetic progression is (S_n=3n^2+2n) then what is the sum of the first (15) terms?The sum of the first (12) terms of an arithmetic progression is (516) and the (12)th term is (75). What is the first term?In an arithmetic progression the first term is (42) and the common difference is (-3). What is the sum of the first (25) terms?For an arithmetic progression (S_n=5n^2-3n). What is the (11)th term?The first term of an arithmetic progression is (18). If the sum of the first (10) terms is (315) then what is the common difference?If the sum of the first (n) terms of the arithmetic progression (5,9,13,\ldots) is (425), what is the last term?In an arithmetic progression (a=6) and (d=7). If (S_n=760), what is (n)?If the sum of the first (18) terms of an arithmetic progression is (999) and the first term is (13), what is the last term?In an arithmetic progression (S_{14}=497) and (S_{13}=429). What is the (14)th term?The (5)th term of an arithmetic progression is (22) and the (15)th term is (62). What is the sum of the first (15) terms?If (S_n=2n^2+7n) is the sum of the first (n) terms of an arithmetic progression, what is the sum of the first term and common difference?How many initial terms of the arithmetic progression (81,75,69,\ldots) have sum (315)?In an arithmetic progression (S_{10}=220) and (S_{20}=840). What is the sum from the (11)th term to the (20)th term?The sum of the first n terms of an arithmetic progression is S_n = n(4n − 1). What is the 20th term?