Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.

If a₁, a₂, a₃, ..., an and b₁, b₂, b₃, ..., bn are arithmetic progressions, then a₁+b₁, a₂+b₂, a₃+b₃, ..., an+ bn is also an arithmetic progression.

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The Answer of Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If a₁, a₂, a₃, ..., an and b₁, b₂, b₃, ..., bn are arithmetic progressions, then a₁+b₁, a₂+b₂, a₃+b₃, ..., an+ bn is also an arithmetic progression.

Determine Whether the Statement Is True or False