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
What is the sum of the first (15) odd natural numbers?EasyLevel 67What is the sum of the first (10) terms of the AP (17,22,27,\ldots)?EasyLevel 67If \(S_n\) is the sum of the first n terms of an arithmetic progression, which relation gives the nth term?EasyLevel 67What will be the sum of the first (5) terms of the AP (60,54,48,\ldots)?EasyLevel 67What is the sum of the first (14) terms of the AP (8,16,24,\ldots)?EasyLevel 67In an auditorium, the first row has 8 seats and each successive row has 3 more seats than the previous row. If there are 12 such rows, what is the total number of seats?EasyLevel 67What will be the sum of the first (18) terms of the AP (5,9,13,\ldots)?EasyLevel 67In an auditorium, the first row has 20 seats and each successive row has 2 more seats. If there are 15 rows in total, what is the correct total number of seats?EasyLevel 67What is the sum of the first (6) terms of the AP (19,29,39,\ldots)?EasyLevel 67What is the sum of the first (22) terms of the AP (32,36,40,\ldots)?EasyLevel 67If an arithmetic progression has first term (a=3), common difference (d=2), and number of terms (n=10), what is the sum of the first (10) terms?EasyLevel 68Find the sum of the first 12 terms of the arithmetic progression (5, 8, 11, ...).EasyLevel 68What is the sum of the first (15) terms of the arithmetic progression (2,6,10,\ldots)?EasyLevel 68If the first term of an arithmetic progression is (7), the last term is (43), and there are (10) terms, what is the sum?EasyLevel 68Find the sum of the first 18 odd natural numbers.EasyLevel 68What will be the sum of the first (25) even natural numbers?EasyLevel 68What is the sum of the first (8) terms of the arithmetic progression (10,15,20,\ldots)?EasyLevel 68If an arithmetic progression has first term \(a\), last term \(l\), and \(n\) terms, which is the correct formula for the sum \(S_n\) of its first \(n\) terms?EasyLevel 68What is the sum of the first 7 terms of the arithmetic progression (12, 10, 8, ...)?EasyLevel 68An arithmetic progression has first term 6, last term 60, and 10 terms. What is its sum?EasyLevel 68