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Write out the first five terms of the sequence [tex]a_n = 4(4n - 3)[/tex].

A. [tex]1, 5, 9, 13, 17[/tex]

B. [tex]4, 8, 12, 16, 20[/tex]

C. [tex]-12, 4, 20, 36, 52[/tex]

D. [tex]4, 20, 36, 52, 68[/tex]

Answer :

To write out the first five terms of the sequence given by the formula [tex]\( a_n = 4(4n - 3) \)[/tex], follow these steps:

1. Find the first term ([tex]\( a_1 \)[/tex]):
- Substitute [tex]\( n = 1 \)[/tex] into the formula:
[tex]\[
a_1 = 4(4 \times 1 - 3) = 4(4 - 3) = 4 \times 1 = 4
\][/tex]

2. Find the second term ([tex]\( a_2 \)[/tex]):
- Substitute [tex]\( n = 2 \)[/tex] into the formula:
[tex]\[
a_2 = 4(4 \times 2 - 3) = 4(8 - 3) = 4 \times 5 = 20
\][/tex]

3. Find the third term ([tex]\( a_3 \)[/tex]):
- Substitute [tex]\( n = 3 \)[/tex] into the formula:
[tex]\[
a_3 = 4(4 \times 3 - 3) = 4(12 - 3) = 4 \times 9 = 36
\][/tex]

4. Find the fourth term ([tex]\( a_4 \)[/tex]):
- Substitute [tex]\( n = 4 \)[/tex] into the formula:
[tex]\[
a_4 = 4(4 \times 4 - 3) = 4(16 - 3) = 4 \times 13 = 52
\][/tex]

5. Find the fifth term ([tex]\( a_5 \)[/tex]):
- Substitute [tex]\( n = 5 \)[/tex] into the formula:
[tex]\[
a_5 = 4(4 \times 5 - 3) = 4(20 - 3) = 4 \times 17 = 68
\][/tex]

After calculating the terms, the first five terms of the sequence are: [tex]\( 4, 20, 36, 52, 68 \)[/tex].

Therefore, the correct answer is option D: [tex]\( 4, 20, 36, 52, 68 \)[/tex].

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