Answer:
[tex]a_2=3[/tex]
Step-by-step explanation:
The arithmetic sequence is given as: [tex]1,\ a_2, \ a_3, \ a_4, \ \cdots,\ a_{10}[/tex]
We are told that the 10 numbers add up to 100.
[tex]S_n=\frac{n}{2}(a_1+l)\\ $Where: \\n=number of terms\\l=last term\\a_1$=first term[/tex]
[tex]S_{10}=100\\100=\dfrac{10}{2}(1+l)\\100=5(1+l)\\$Divide both sides by 5$\\20=1+l\\$Last term, $l=20-1=19[/tex]
We know that the nth term of an arithmetic sequence
[tex]l=a_1+(n-1)d\\19=1+(10-1)d\\19=1+9d\\9d=19-1\\9d=18\\d=2[/tex]
Therefore, the second number
[tex]a_2=a_1+2\\=1+2\\a_2=3[/tex]
