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 first term of an arithmetic progression is (3) and the last term is (103). If the sum is (901), how many terms are there?What is the average of the first (18) terms of the arithmetic progression (12,19,26,\ldots)?In an arithmetic progression, a = 25 and d = −2. What is the sum of the first 20 terms?If the sum of the first (9) terms of an arithmetic progression is (279) and the sum of the first (18) terms is (1044), what is the sum of the first (27) terms?In an arithmetic progression (a=4) and the sum of the first (16) terms is (904). What is the (16)th term?In an arithmetic progression the first term is (9) and the common difference is (4). What is the sum of the first (30) terms?In an arithmetic progression (a=11) and (d=6). If (S_n=1003), what is (n)?In a decreasing arithmetic progression the first term is (65) and the common difference is (-5). What is the sum of the first (15) terms?The (7)th term of an arithmetic progression is (34) and the (18)th term is (89). What is the sum of the first (18) terms?If the sum of the first (n) terms of an arithmetic progression is (S_n=4n^2+3n), what is the (25)th term?The first term of an arithmetic progression is (12) and the sum of the first (10) terms is (345). What is the common difference?The first term of an arithmetic progression is (7) and the last term is (151). If the total sum is (1264), how many terms are there?In the arithmetic progression (14,20,26,\ldots), what is the sum from the (5)th term to the (20)th term?If (S_n=3n^2-2n) for an arithmetic progression, what is its common difference?For the arithmetic progression (120,113,106,\ldots), the sum of how many initial terms will remain positive?The sum of the first (n) odd natural numbers is (576). What is (n)?What is the sum of the multiples of (7) from (21) to (210)?What is the sum of the integers divisible by (9) between (50) and (200)?In an arithmetic progression (S_{12}=294) and (S_{24}=1020). What is (S_{36})?In an arithmetic progression (t_3+t_9=70) and (t_5+t_{15}=110). What is the sum of the first (20) terms?