Answer:
n = 17
Step-by-step explanation:
Method 1
The difference between the 5th and 6th terms is 13 - 11 = 2
Therefore, the next term can be found by adding 2 each time.
If we continue with this sequence, we get:
5 = 11
6 = 13
7 = 13 + 2 = 15
8 = 15 + 2 = 17
9 = 17 + 2 = 19
10 = 19 + 2 = 21
So n = 17
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Method 2
Arithmetic sequence
General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
where:
- [tex]a_n[/tex] is the nth term
- a is the first term
- d is the common difference between terms
Given terms of the sequence:
[tex]a_5=11\\a_6=13\\a_8=n\\a_{10}=21[/tex]
The common difference can be found by subtracting one term from the next term:
[tex]d=13-11=2[/tex]
To find a, substitute the found value of d into the equation for one of the given terms:
[tex]\begin{aligned}a_5 =a+(5-1)2 & =11\\ a+8 & =11\\ a & = 3\end{aligned}[/tex]
Therefore, the formula to find the nth term is:
[tex]\implies a_n=3+(n-1)2[/tex]
[tex]\implies a_n=2n+1[/tex]
So, the 8th term is:
[tex]\implies a_8=2(8)+1=17[/tex]
