To solve for the nth term of the sequence given by [tex]\( a_n = n^2 - 1 \)[/tex] and find [tex]\( a_n \)[/tex] when [tex]\( n = 3 \)[/tex], follow these steps:
1. Identify the given formula:
The nth term of the sequence is given by:
[tex]\[
a_n = n^2 - 1
\][/tex]
2. Substitute the given value of [tex]\( n \)[/tex] into the formula:
We need to find the value of [tex]\( a_n \)[/tex] when [tex]\( n = 3 \)[/tex]. Substitute [tex]\( n = 3 \)[/tex] into the formula:
[tex]\[
a_3 = 3^2 - 1
\][/tex]
3. Calculate the exponentiation:
Here, [tex]\( 3^2 \)[/tex] means [tex]\( 3 \times 3 \)[/tex], which equals 9. So,
[tex]\[
a_3 = 9 - 1
\][/tex]
4. Perform the subtraction:
Subtract 1 from 9 to find the value of [tex]\( a_n \)[/tex] when [tex]\( n = 3 \)[/tex]:
[tex]\[
a_3 = 9 - 1 = 8
\][/tex]
Therefore, the 3rd term of the sequence is [tex]\( a_3 = 8 \)[/tex].
