To find the 5th term of an Arithmetic Progression where the [tex]\( n^{\text{th}} \)[/tex] term is given by the formula [tex]\( a_n = 4n + 5 \)[/tex], you can follow these steps:
1. Identify the formula given for the [tex]\( n^{\text{th}} \)[/tex] term of the sequence:
[tex]\[
a_n = 4n + 5
\][/tex]
2. To find the 5th term, we need to substitute [tex]\( n = 5 \)[/tex] into the formula.
3. Substitute [tex]\( n = 5 \)[/tex] into the formula:
[tex]\[
a_5 = 4(5) + 5
\][/tex]
4. Perform the multiplication inside the parentheses:
[tex]\[
a_5 = 4 \times 5 + 5
\][/tex]
5. Calculate the result of the multiplication:
[tex]\[
a_5 = 20 + 5
\][/tex]
6. Finally, add the two numbers:
[tex]\[
a_5 = 25
\][/tex]
Therefore, the 5th term of this Arithmetic Progression is [tex]\( 25 \)[/tex].
