For the following exercises, write an explicit formula for each sequence. 4, 7, 12, 19, 28, …

For the following exercises, write an explicit formula for each sequence.

4, 7, 12, 19, 28, …

Expert Solution

Consider the sequence given below:

{4, 7, 12, 19, 28, …}

The objective is to write the explicit formula for each sequence.

In the given sequence, all terms are positive.

Consider the numerical values of the terms and express them as follows:

4 = 1 + 3

= 12 + 3

7 = 4 + 3

= 22 + 3

Furthermore,

12 = 9 + 3

= 32 + 3

19 = 16 + 3

= 42 + 3

Also,

28 = 25 + 3

= 52 + 3

…

Hence, the terms of the given sequence are obtained by adding 3 to the squares of natural numbers.

So, they will be represented by n2 + 3.

Therefore, the explicit formula for the nth term of given sequence will be an = n2 + 3.

Junaid answered 1 year ago

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Question

For the following exercises, write an explicit formula for each sequence. 4, 7, 12, 19, 28, …

Solutions

Expert Solution

Related Solutions

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