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Reset your password if you forgot it. Problem 1An arithmetic progression consists of three terms whose sum is 48 and the sum of their squares is 800. Problem 2If the 6-th term of an arithmetic progression is 121, find the sum of the first 11 terms. Problem 3The sum of the first 5 terms of an AP is 30 and the fourth term is 44. Find the common difference and the sum of the first 10 terms.
Let “x” be the THIRD term and “d” be the common difference. 2d, and their sum is 5x. So, you just found the third term. Problem 5The sum of the fifth and seventh terms of an arithmetic series is 38, while the sum of the first fifteen terms is 375. Determine the first term and the common difference. Problem 6If 7 times the 7-th term of an AP is equal to 11 times its 11-th term, show that its 18-th term is 0. Problem 7The sum of the first five terms of an arithmetic progression is 10, the sum of their squares is 380.
Find the first term and common difference. Let x be the third term of our arithmetic progression and d be its common difference. The sum of these terms is 5x. One root of this equation is 2. Find x and the sum of the first 10 terms. OVERVIEW of my lessons on arithmetic progressions with short annotations is in the lesson OVERVIEW of lessons on arithmetic progressions. ALGEBRA-II – YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-II.
This lesson has been accessed 1472 times. Password: Register in one easy step! Reset your password if you forgot it. This lesson presents some basic and typical problems on arithmetic progressions. Problem 1Derive the formula for the sum of the first n natural numbers. The sequence of the first n natural numbers is 1, 2, 3, 4, 5, , n-1, n.
This is the arithmetic progression with the first term and the common difference . This is the formula for the sum of the first n natural numbers we are looking for. Using this formula you can easily calculate the partial sums of the sequence of the natural numbers. 1, 2, 3, 4, 5, 6, .