# Arithmetic Progressions: Problems with Solutions

Problem 1
What is the common difference of the arithmetic progression 10, 5, 0, -5?
Problem 2
Do the numbers 2, 6, 10, 12, 16... form an arithmetic progression?
Problem 3 sent by Roy K Behanan
Find the 10th term of the arithmetic progression 1, 3.5, 6, 8.5,...
Problem 4
Find the sum of the first 10 natural numbers.
Problem 5 sent by Taz
The sum of five consecutive numbers is 100. Find the first number.
Problem 6
Let $${a_n}$$ be an arithmetic progression. If $$a_1=4$$ and $$a_2=7$$, determine $$a_{11}$$
Problem 7
Let $${a_n}$$ be an arithmetic progression, for which $$d=12$$ and $$a_3=43$$. Find $$a_1$$
Problem 8
Let $$a_n$$ be an arithmetic progression. If $$a_1=15$$ and $$a_2=8$$, determine $$a_{19}$$.
Problem 9
Let $${a_n}$$ be an arithmetic progression, for which the first term $$a_1=1$$ and common difference $$d=1$$. Find $$a_{1083}$$
Problem 10
Let $${a_n}$$ be an arithmetic progression, for which $$a_2=5$$ and $$a_1=-11$$. Find the difference of the progression.

Problem 11
Determine the difference of an arithmetic progression $${a_n}$$, if $$a_5=18$$ and $$a_2=9$$
Problem 12
Let $${a_n}$$ be an arithmetic progression, for which $$a_3=13$$ and $$a_{11}=25$$. Find $$a_7$$
Problem 13
Let $${a_n}$$ be an arithmetic progression, for which $$a_1=15$$ and $$d=3$$. Find the sum of the first 10 elements.
Problem 14
What is the common ratio of the geometric progression 3, -6, 12, -24, 48...?
Problem 15
Let $${a_n}$$ be an arithmetic progression. If $$a_1=7$$ and $$d=4$$, determine the sum of the first 6 elements with even indexes.

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