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Use the given [tex]$n$[/tex]th term formula to compute the first five terms of the sequence.

[tex]\[
\begin{array}{l}
a_n = 6n^2 - 4n \\
a_1 = \square \\
a_2 = \square \\
a_3 = \square \\
a_4 = \square \\
a_5 = \square
\end{array}
\][/tex]



Answer :

GinnyAnswer
To find the first five terms of the sequence given by the formula [tex]\( a_n = 6n^2 - 4n \)[/tex], we will substitute [tex]\( n \)[/tex] with 1, 2, 3, 4, and 5 respectively.

1. Calculate [tex]\( a_1 \)[/tex]:
[tex]\[ a_1 = 6 \cdot 1^2 - 4 \cdot 1 \][/tex]
[tex]\[ a_1 = 6 \cdot 1 - 4 \][/tex]
[tex]\[ a_1 = 6 - 4 \][/tex]
[tex]\[ a_1 = 2 \][/tex]

2. Calculate [tex]\( a_2 \)[/tex]:
[tex]\[ a_2 = 6 \cdot 2^2 - 4 \cdot 2 \][/tex]
[tex]\[ a_2 = 6 \cdot 4 - 4 \cdot 2 \][/tex]
[tex]\[ a_2 = 24 - 8 \][/tex]
[tex]\[ a_2 = 16 \][/tex]

3. Calculate [tex]\( a_3 \)[/tex]:
[tex]\[ a_3 = 6 \cdot 3^2 - 4 \cdot 3 \][/tex]
[tex]\[ a_3 = 6 \cdot 9 - 4 \cdot 3 \][/tex]
[tex]\[ a_3 = 54 - 12 \][/tex]
[tex]\[ a_3 = 42 \][/tex]

4. Calculate [tex]\( a_4 \)[/tex]:
[tex]\[ a_4 = 6 \cdot 4^2 - 4 \cdot 4 \][/tex]
[tex]\[ a_4 = 6 \cdot 16 - 4 \cdot 4 \][/tex]
[tex]\[ a_4 = 96 - 16 \][/tex]
[tex]\[ a_4 = 80 \][/tex]

5. Calculate [tex]\( a_5 \)[/tex]:
[tex]\[ a_5 = 6 \cdot 5^2 - 4 \cdot 5 \][/tex]
[tex]\[ a_5 = 6 \cdot 25 - 4 \cdot 5 \][/tex]
[tex]\[ a_5 = 150 - 20 \][/tex]
[tex]\[ a_5 = 130 \][/tex]

Therefore, the first five terms of the sequence are:
[tex]\[ a_1 = 2, \quad a_2 = 16, \quad a_3 = 42, \quad a_4 = 80, \quad a_5 = 130. \][/tex]

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