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
In an arithmetic progression, the sum of the first and last terms is (144), and there are (18) terms. What will be the sum of the progression?Find the sum of all two-digit positive numbers divisible by (4).What is the sum of all three-digit multiples of (25) less than (300)?If the (n)th term of an arithmetic progression is (a_n=5n+4), find the sum of the first (20) terms.If (a_n=7n-9), what will be the sum of the first (18) terms?If the (n)th term of an arithmetic progression is (a_n=3n+10), what is the sum of the first (16) terms?If (a_n=50-2n), find the sum of the first (14) terms.In a savings plan, the monthly deposit is (45,65,85,\ldots) rupees. What will be the total saving in the first (12) months?In a ground, rows of chairs follow (80,115,150,\ldots). How many chairs will there be in the first (10) rows?In a construction work, rows of bricks follow (25,37,49,\ldots). How many bricks will be used in the first (18) rows?What is the sum of the first 5 terms of the arithmetic progression (2,7,12,17, …)?What is the sum of the first (5) terms of the arithmetic progression (7,15,23,31,\ldots)?What is the sum of the first 12 terms of the arithmetic progression (5, 9, 13, 17, …)?What is the sum of the first 9 terms of the arithmetic progression (8, 14, 20, 26, …)?What is the sum of the first 16 terms of the arithmetic progression (4, 9, 14, 19, …)?In an AP, the first term is (3), common difference is (5), and number of terms is (20). What is the sum of the first (20) terms?If an AP has (a=12), (d=-2), and (n=15), find the value of (S_{15}).What is the sum of the first (25) positive odd numbers?Find the sum of all positive multiples of (7) from (7) to (140).What is the sum of the first (30) terms of the AP (-5,-2,1,\ldots)?