Answer:
88
Step-by-step explanation:
airthmetic sequences are linear.
This means no matter what two points you choose from an arithmetic sequence the slope (the common difference,d) will be constant.
[tex]\frac{a_{22}-a_1}{22-1}=d[/tex]
[tex]\frac{a_{22}-4}{22-1}=4[/tex]
[tex]\frac{a_{22}-4}{21}=4[/tex]
Multiply both sides by 21:
[tex]a_{22}-4=21(4)[/tex]
[tex]a_{22}-4=84[/tex]
Add 4 on both sides:
[tex]a_{22}=88[/tex]
The 22nd term is 88.
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Or the explicit form for an arithmetic sequence is:
[tex]a_n=a_1+d(n-1)[/tex]
[tex]a_n=4+4(n-1)[/tex]
We want to know the 22nd term which means we need to replace n with 22:
[tex]a_{22}=4+4(22-1)[/tex]
[tex]a_{22}=4+4(21)[/tex]
[tex]a_{22}=4+84[/tex]
[tex]a_{22}=88[/tex]
