Answer:
See Explanation
Step-by-step explanation:
The question is incomplete. However, the available details is enough to work out a solution.
Considering the first even number: 2
In this case, n = 1
The sum of the first even term is 2.
Represent the sum as a product:
[tex]2 = 1 * 2[/tex]
Considering the first two even numbers: 2 and 4
In this case, n = 2
The sum of the first two even terms is 6
Represent the sum as a product:
[tex]6 = 2 * 3[/tex]
Considering the first three even numbers: 2, 4 and 6
In this case, n = 3
The sum of the first two even terms is 12
Represent the sum as a product:
[tex]12 = 3 * 4[/tex]
Notice the pattern from n = 1 to 3
[tex]2 = 1 * 2[/tex] --- n = 1
[tex]6 = 2 * 3[/tex] --- n = 2
[tex]12 = 3 * 4[/tex] --- n = 3
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It follows that, the sum when represented as a product is: [tex]n * (n + 1)[/tex]
So, the sum of the first 52 even terms would be:
[tex]52 * (52 + 1)[/tex]
Where n = 52
[tex]52 * (52 + 1) = 52 * 53[/tex]
[tex]52 * (52 + 1) = 2756[/tex]
Hence, the sum of the first 52 even terms is 52 * 53 or 2756
