# Arithmetic progression solved problems

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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, .