# 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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