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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

Find the sum of all numbers from (1) to (700) that are divisible by (4) or (7).HardLevel 68Find the sum of all two-digit numbers that leave remainder (5) when divided by (6).HardLevel 68The (7)th term of an AP is (48), and the sum of the first (7) terms is (231). Find the sum of the first (14) terms.HardLevel 68The first term of an AP is x, and the common difference is 2x + 1. If the sum of the first 10 terms is 445, what is the value of x?HardLevel 68Find the sum of all numbers from (250) to (1000) that are divisible by (12) but not by (18).HardLevel 68If in an AP (S_6=81) and (S_{12}=342), what is the value of (S_{24})?HardLevel 68Find the sum of all numbers from (1) to (1000) that are divisible by (6) but not by (15).HardLevel 68If the sum of an AP is S_n = 6n² + n, find the sum from the 31st term to the 45th term.HardLevel 68In an AP, the sum of the first (25) terms is (1625), and the (25)th term is (113). Find the first term.HardLevel 68The sum of the first term and the (40)th term of an AP is (210). Find the sum from the (11)th term to the (30)th term.HardLevel 68In an AP, (a=23), (d=9), and (n=26). Find the sum of the first (26) terms.HardLevel 69In the AP (8,14,20,\ldots), what is the sum from the (18)th term to the (36)th term?HardLevel 69Find the sum of the AP (-12,-5,2,\ldots,184).HardLevel 69Find the sum of all numbers divisible by (17) from (150) to (750).HardLevel 69In a saving plan, (3200) rupees are deposited in the first month and (225) rupees more every next month. What is the total deposit in (30) months?HardLevel 69Find the sum of all three-digit numbers divisible by (19).HardLevel 69Find the sum of the first (22) terms of the AP (160,151,142,\ldots).HardLevel 69If (S_n=6n^2-5n), find the sum from the (31)st term to the (50)th term.HardLevel 69In an AP, (S_{16}=736) and (S_{32}=2752). Find the value of (S_{48}).HardLevel 69Find the sum of the first (25) terms of the AP (140,132,124,\ldots).HardLevel 69