Answer:
a₁₀₀ = 385
Step-by-step explanation:
The nth term of arithmetic sequence is [tex]a_n=a_1+d(n-1)[/tex]
So:
[tex]a_9=a_1+d(9-1)\\\\37=a_1+8d\\\\a_1=37-8d\\\\\\a_{16}=a_1+d(16-1)\\\\65=a_1+15d\\\\65=37-8d+15d\\\\28=7d\\\\d=4\\\\a_1=37-8\cdot4=5\\\\\\a_{100}=a_1+d(100-1)=5+4\cdot95=385[/tex]
