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 average of the first (40) terms of an arithmetic progression is (80) and the first term is (2). What is the common difference?In an arithmetic progression the first term is (13) and the common difference is (7). What is the sum of the first (22) terms?In an arithmetic progression (a=18) and (d=-4). How many first terms have sum (144)?If the sum of the first n terms of an arithmetic progression is S_n = 5n² + 4n, what is the 18th term?The (9)th term of an arithmetic progression is (46) and the (21)th term is (106). What is the sum of the first (21) terms?In an arithmetic progression (S_{10}=310) and (S_{20}=1120). What is the sum from the (11)th term to the (20)th term?What is the sum of numbers divisible by (12) between (75) and (255)?The first term of an arithmetic progression is (19) and (S_{15}=810). What is the (15)th term?The sum of the first (n) terms of the arithmetic progression (8,13,18,\ldots) is (775). What is (n)?If (S_n=4n^2-n) is the sum of an arithmetic progression, what is the sum of the first (12) terms?In an arithmetic progression (S_6=93) and (S_{12}=366). What is (S_{18})?In an arithmetic progression (t_{12}=51) and (S_{12}=336). What is the first term?What is the sum of all three-digit numbers divisible by (17)?In an arithmetic progression the first term is (25) and the common difference is (-2). What is the average of the first (20) terms?If the sum of the first \(n\) terms of a sequence is \(S_n=3n^2+2n\), which of the following statements is correct?If S_n = 6n² + 2n, what is a + d for this arithmetic progression?What is the maximum value of the sum of initial terms of the arithmetic progression (100,94,88,\ldots)?What is the sum of natural numbers from (1) to (150) that are not divisible by (6)?In an arithmetic progression (S_{14}=777) and (t_{14}=96). What is the first term?If an arithmetic progression has first term \(a\) and \(n\)th term \(l\), which is the correct formula for the sum of its first \(n\) terms?