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 [tex]{a_n}[/tex] be an arithmetic progression, for which [tex]a_1=15[/tex] and [tex]d=3[/tex]. Find the sum of the first 10 elements.
Problem №5
Let [tex]{a_n}[/tex] be an arithmetic progression, for which [tex]a_3=13[/tex] and [tex]a_{11}=25[/tex]. Find [tex]a_7[/tex]
Problem №6
Determine the difference of an arithmetic progression [tex]{a_n}[/tex], if [tex]a_5=18[/tex] and [tex]a_2=9[/tex]
Problem №7
Let [tex]{a_n}[/tex] be an arithmetic progression, for which [tex]a_2=5[/tex] and [tex]a_1=-11[/tex]. Find the difference of the progression.
Problem №8
Let [tex]{a_n}[/tex] be an arithmetic progression, for which [tex]a_1=1[/tex] and [tex]d=1[/tex]. Find [tex]a_{1083}[/tex]
Problem №9
Let [tex]a_n[/tex] be an arithmetic progression. If [tex]a_1=15[/tex] and [tex]a_2=8[/tex], determine [tex]a_{19}[/tex].
Problem №10
Let [tex]{a_n}[/tex] be an arithmetic progression, for which [tex]d=12[/tex] and [tex]a_3=43[/tex]. Find [tex]a_1[/tex]
Problem №11
Let [tex]{a_n}[/tex] be an arithmetic progression. If [tex]a_1=4[/tex] and [tex]a_2=7[/tex], determine [tex]a_{11}[/tex]
Problem №12
Let [tex]{a_n}[/tex] be an arithmetic progression. If [tex]a_1=7[/tex] and [tex]d=4[/tex], determine the sum of the first 6 elements with even indexes.
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