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
If an arithmetic progression has (S_8=228) and (S_{17}=1020), what is the sum of the (9)th to (17)th terms?In an arithmetic progression, S₆ = 165 and S₁₄ = 665. Find the sum of the 7th to 14th terms.If (S_5=30) and (S_{12}=408), what will be the sum of the (6)th to (12)th terms?In an arithmetic progression, (S_9=342) and (S_{20}=1640). What will be the sum of the (10)th to (20)th terms?In the arithmetic progression (6,14,22,\ldots), the sum of how many first terms will be (930)?In the arithmetic progression (10,19,28,\ldots), the sum of how many first terms will be (1240)?In the arithmetic progression (5,16,27,\ldots), the sum of how many first terms will be (1230)?In the arithmetic progression (4,16,28,\ldots), the sum of how many first terms will be (1504)?Find the sum of the numbers divisible by (9) between (120) and (300).What is the sum of the numbers divisible by (14) between (100) and (350)?Find the sum of the numbers divisible by (15) between (50) and (250).What will be the sum of the numbers divisible by (16) between (200) and (500)?If the sum of the first (n) odd natural numbers is (625), what will be the value of (n)?If the sum of the first (n) even natural numbers is (756), find the value of (n).After removing the first (14) odd natural numbers from the first (26) odd natural numbers, what will be the sum of the remaining numbers?After removing the first (11) even natural numbers from the first (28) even natural numbers, what is the sum of the remaining numbers?The average of the first (15) terms of an arithmetic progression is (64). What will be the sum of these (15) terms?The sum of the first (18) terms of an arithmetic progression is (1170). What will be the average of these terms?The sum of the first (12) terms is (912), and the first term is (18). What will be the last term (l)?The sum of the first (15) terms is (975), and the last term is (97). What is the first term?