# Arithmetic Progressions - Problems with Solutions

Problem №1 sent by Roy K Behanan
Find the 10th term of the arithmetic progression 1, 3.5, 6, 8.5,...
Problem №2
Find the sum of the first 10 natural numbers.
Problem №3 sent by Taz
The sum of five consecutive numbers is 100. Find the first number.
Problem №4
Let ${a_n}$ be an arithmetic progression, for which $a_1=15$ and $d=3$. Find the sum of the first 10 elements.
Problem №5
Let ${a_n}$ be an arithmetic progression, for which $a_3=13$ and $a_{11}=25$. Find $a_7$
Problem №6
Determine the difference of an arithmetic progression ${a_n}$, if $a_5=18$ and $a_2=9$
Problem №7
Let ${a_n}$ be an arithmetic progression, for which $a_2=5$ and $a_1=-11$. Find the difference of the progression.
Problem №8
Let ${a_n}$ be an arithmetic progression, for which $a_1=1$ and $d=1$. Find $a_{1083}$
Problem №9
Let $a_n$ be an arithmetic progression. If $a_1=15$ and $a_2=8$, determine $a_{19}$.
Problem №10
Let ${a_n}$ be an arithmetic progression, for which $d=12$ and $a_3=43$. Find $a_1$
Problem №11
Let ${a_n}$ be an arithmetic progression. If $a_1=4$ and $a_2=7$, determine $a_{11}$
Problem №12
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.