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The [tex]n^{\text{th}}[/tex] term of an Arithmetic Progression is [tex]a_n = 4n + 5[/tex]. Find its [tex]5^{\text{th}}[/tex] term.

Sagot :

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].
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