Question

Enter the first 4 terms of the sequence defined by the given rule. assume that the domain of each function is the set of whole numbers greater than 0. f(n) = (2n + 2)2 the first 4 terms of the sequence are , , , and .

Answer 1

The first four terms of the sequence are 8,12,16 and 20.

What is a Sequence?

• A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms).
• The length of the series is the number of elements (potentially infinite). In contrast to a set, the same items might appear more than once in a sequence at various points, and unlike a set, the order is important.
• A sequence can be described formally as a function from natural numbers (the positions of the sequence's elements) to the items at each of those positions.
• An indexed family, which is a function from an index set that may not be a set of numbers to another set of elements, can be thought of as a generalization of the idea of a sequence.

Given the function is f(n) = (2n+2)2

Now, we want first four terms, therefore, putting 1, 2, 3, 4 in the sequence we get:

f(1) = (2*1+2)2 = 8

f(2) = (2*2+2)2 = 12

f(3) = (2*3+2)2 = 16

f(4) = (2*4+2)2 = 20

Hence, The first four terms of the sequence are 8,12,16 and 20.

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