Mathematics

# "What is the first term of a 10 term arithmetic series with T2= 10 and S = 120? Leave answer in exact form"

$t_{1}\\ t_{2}=t_{1}+a=10\\ t_{3}=t_{1}+2a\\ t_{4}=t_{1}+3a\\ ...\\ t_{10}=t_{1}+9a\\ s=120=t_{1}+(t_{1}+a)+(t_{1}+2a)+(t_{1}+3a)+...+(t_{1}+9a)\\ =10*t_{1}+a(0+1+2+3+...+9)\\ =10*(t_{2}-a)+a*\frac{10*9}{2}\\ =10(10-a)+45a\\ ==\ \textgreater \ 10(10-a)+45a=120\\ ==\ \textgreater \ 2(10-a)+9a=24\\ ==\ \textgreater \ 7a=4\\ ==\ \textgreater \ a=\frac{4}{7}$