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
Find the sum of the first (14) terms of the arithmetic progression (6,9,12,\ldots).EasyLevel 69If an arithmetic progression has first term (4), common difference (5), and (13) terms, what is the sum of the first (13) terms?EasyLevel 69What is the sum of the first (10) terms of the arithmetic progression (15,19,23,\ldots)?EasyLevel 69What is the sum of the first (22) natural numbers?EasyLevel 69Find the sum of the first (15) odd natural numbers.EasyLevel 69What will be the sum of the first (19) even natural numbers?EasyLevel 69If the first term of an arithmetic progression is 8, the last term is 62, and there are 10 terms, what is the sum?EasyLevel 69Find the sum of the first 8 terms of the arithmetic progression (40, 36, 32, ...).EasyLevel 69What will be the sum of the first (9) terms of the arithmetic progression (7,12,17,\ldots)?EasyLevel 69In an auditorium, rows of seats follow (9,12,15,\ldots). How many seats will there be in the first (12) rows?EasyLevel 69If (S_6=72) and (S_{12}=252), what is the sum of the (7)th to (12)th terms?EasyLevel 69What is the sum of the first (11) terms of the arithmetic progression (3,10,17,\ldots)?EasyLevel 69The average of the first (8) terms of an arithmetic progression is (27). What is the sum of these (8) terms?EasyLevel 69Find the sum of the first (15) terms of the arithmetic progression (18,22,26,\ldots).EasyLevel 69A student solves (4,8,12,\ldots) practice questions per day. How many questions will be solved in the first (10) days?EasyLevel 69If an arithmetic progression has (a=20), (d=-3), and (n=7), what is the sum of the first (7) terms?EasyLevel 69What is the sum of the first (12) terms of the arithmetic progression (25,30,35,\ldots)?EasyLevel 69What will be the sum of the first (13) odd natural numbers?EasyLevel 69If a_n = 3n + 2, find the sum of the first 5 terms.EasyLevel 69In a savings plan, the monthly deposit is (200,250,300,\ldots) rupees. What is the total amount for the first (8) months?EasyLevel 69