[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]
▪ [tex]\bm{1.) 2, 4, 6, 8,...}[/tex]
▪ [tex]\bm{2.) 3, 6, 10, 15,...}[/tex]
▪ [tex]\bm{3.) -3,-1, 1, 3,...}[/tex]
▪ [tex]\bm{4.) 5, 10, 20,40,...}[/tex]
▪ [tex]\bm{5.) 10, 6, 2,-2,...}[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{ Required:}}}}}}[/tex]
To determine whether it is [tex]\bold{Arithmetic \: \: Sequence}[/tex] or not.
[tex]{\large{\textsf{\textbf{\underline{\underline{ Explanation:}}}}}}[/tex]
‣ An arithmetic sequence is arithmetic if the difference between any term and the previous one is constant.
1.) [tex]\tt{2, 4, 6, 8,... }[/tex]
[tex]\tt{ 4-2=2}[/tex]
[tex]\tt{6-4=2 }[/tex]
[tex]\Longrightarrow\tt{ 8-6=2}[/tex]
[tex]\boxed{ \red{ \tt{Arithmetic \: \: Sequence }}}\large{✓}[/tex]
2.) [tex]\tt{3, 6, 10, 15,... }[/tex]
[tex]\tt{ 6-3=3}[/tex]
[tex]\Longrightarrow\tt{ 10-6=4}[/tex]
[tex]\boxed{ \red{ \tt{ Not \: \: an \: Arithmetic \: \: Sequence }}}\large{✗}[/tex]
3.) [tex]\tt{ -3,-1, 1, 3,...}[/tex]
[tex]\tt{ - 1 - ( - 3) = - 1 + 3 = 2 }[/tex]
[tex]\tt{1( - 1) = 1 + 1 = 2 }[/tex]
[tex]\Longrightarrow\tt{3-1=2 }[/tex]
[tex]\boxed{ \red{ \tt{ Arithmetic \: \: Sequence}}}\large{✓}[/tex]
4.) [tex]\tt{5, 10, 20,40,... }[/tex]
[tex]\tt{10-5=5 }[/tex]
[tex]\Longrightarrow\tt{ 20-10=10}[/tex]
[tex]\boxed{ \red{ \tt{ Not \: \: an \: Arithmetic \: \: Sequence }}}\large{✗}[/tex]
5.) [tex]\tt{10, 6, 2,-2,... }[/tex]
[tex]\tt{ 6-10=-4}[/tex]
[tex]\tt{2-6=-4 }[/tex]
[tex]\Longrightarrow\tt{-2-2=-4 }[/tex]
[tex]\boxed{ \red{ \tt{ Arithmetic \: \: Sequence}}}\large{✓}[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{ Answer:}}}}}}[/tex]
[tex]\sf{1.) \: \: \boxed{ \sf{Yes }}}[/tex] ✓
[tex]\sf{2.) \: \: \boxed{ \sf{No }}}[/tex] ✗
[tex]\sf{3.) \: \: \boxed{ \sf{Yes }}}[/tex] ✓
[tex]\sf{4.) \: \: \boxed{ \sf{No }}}[/tex] ✗
[tex]\sf{5.) \: \: \boxed{ \sf{Yes }}}[/tex] ✓
hope it helps ~
