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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 sum of the first (18) terms is (441), and the first term is (3). If the sequence is an AP, what is the common difference (d)?If an AP has first term \(a\), \(n\)th term \(l\), and \(n\) terms, which is the correct formula for the sum \(S_n\) of its first \(n\) terms?Find the sum of all numbers divisible by (5) between (100) and (200).If the sum of the first (n) terms of the AP (13,18,23,\ldots) is (253), what is (n)?What is the sum of the first (30) terms of the AP (1,4,7,\ldots)?The lengths of rods in a ladder are (40,43,46,\ldots) cm. What is the total length of the first (15) rods?Which of the following formulas can represent \(S_n\), the sum of the first \(n\) terms of an arithmetic progression (AP)?In an AP, (a=17), (d=2), and (S_n=580). Find (n).Find the sum of the first (12) terms of the AP (100,95,90,\ldots).If the sum of the first n natural numbers is 465, what is n?Find the sum of the AP (8,13,18,\ldots,83).A student starts with (15) minutes of practice per day and increases it by (5) minutes every day. What is the total practice time in (14) days?If (S_{25}=1225) and (S_{24}=1128), what is the (25)th term?What is the sum of the first (16) terms of the AP (24,21,18,\ldots)?If an AP has (S_{12}=390) and (d=5), what is the first term (a)?What is the sum of all positive multiples of (4) less than (50)?In the AP 5, 9, 13, ..., how many first terms have sum 434?On a road, the distances of intervals are (6,12,18,\ldots) meters. What is the total distance of the first (25) intervals?If (S_n=5n^2-n), what is the value of (S_9)?Find the sum of the AP (7, 12, 17, ..., 82).