Consider the arithmetic sequence 4,12,20.a, Prove that the sum of consecutive terms of this sequence (starting from the first term) is always a perfect square
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Step-by-step explanation:
There are an infinite number, but the first that comes to mind is this one:
F(n) = 2n - 1
To find each value, you double the value of the term number and subtract one. That gives us these terms, with addition demonstrated to show you can add any number of terms (starting with the first) and get a square.
1, 3, 5, 7, 9… (1 + 3 = 4, 1 + 3 + 5 = 9, 1 + 3 + 5 + 7 = 16, etc.)
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