To find [tex]\( a_6 \)[/tex] given the formula [tex]\( a_n = \frac{1}{2} n + 1 \)[/tex], follow these steps:
1. Identify the given formula and the value of [tex]\( n \)[/tex]. The formula provided is [tex]\( a_n = \frac{1}{2} n + 1 \)[/tex]. The value given for [tex]\( n \)[/tex] is 6.
2. Substitute the value of [tex]\( n \)[/tex] into the formula. Here, [tex]\( n = 6 \)[/tex].
[tex]\[
a_6 = \frac{1}{2} \cdot 6 + 1
\][/tex]
3. Perform the multiplication first, following the order of operations (PEMDAS/BODMAS rules).
[tex]\[
\frac{1}{2} \cdot 6 = 3
\][/tex]
4. Then, add the result to 1.
[tex]\[
a_6 = 3 + 1
\][/tex]
5. Finally, perform the addition.
[tex]\[
a_6 = 4
\][/tex]
Therefore, the value of [tex]\( a_6 \)[/tex] is 4.
