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 first term of an arithmetic progression is (14) and the sum of the first (16) terms is (824). What is the common difference?The first term of an arithmetic progression is (8) and the last term is (176). If the total sum is (2208), how many terms are there?In the arithmetic progression (18,25,32,\ldots), what is the sum from the (8)th term to the (26)th term?If (S_n=4n^2+n) for an arithmetic progression, what is its common difference?For the arithmetic progression (150,141,132,\ldots), the sum of how many initial terms will remain positive?The sum of the first (n) positive even numbers is (650). What is (n)?What is the sum of the multiples of (11) from (44) to (297)?What is the sum of the integers divisible by (14) between (100) and (350)?In an arithmetic progression (S_9=189) and (S_{18}=702). What is (S_{27})?In an arithmetic progression (t_4+t_{10}=68) and (t_7+t_{17}=128). What is the sum of the first (20) terms?The average of the first (30) terms of an arithmetic progression is (76) and the first term is (18). What is the common difference?In an arithmetic progression, the first term is 9 and S₆ : S₁₂ = 2 : 7. What is the common difference?In an arithmetic progression (d=7) and the sum of the (13)th to (24)th terms is (1602). What is the first term?What is the sum of all three-digit numbers divisible by (19)?What is the sum of natural numbers from (1) to (140) that are not divisible by (7)?For the arithmetic progression (4,9,14,\ldots), after how many first terms will the sum exceed (1500) for the first time?In an arithmetic progression (t_{15}=65) and (S_{15}=555). What is the common difference?In an arithmetic progression (a=7) and (S_5:S_{15}=1:7). What is the common difference?The sums of the first (n) terms of the arithmetic progressions (10,14,18,\ldots) and (22,24,26,\ldots) are equal. What is the positive value of (n)?If (S_n=3n^2+4n) for an arithmetic progression, what is the sum from the (16)th to the (25)th terms?