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Recognize to use 2 equations

u_{n}=u_{1}+(n-1)d

6=u_{1}+(5-1)d

6=u_{1}+4d

6-4d=u_{1}- first equation

S_{n}=\frac{n}{2}(2u_{1}+(n-1)d)

30=\frac{6}{2}(2u_{1}+(6-1)d)

10=(2u_{1}+5d)-second equation

Substitute the first equation into the second

10=(2(6-4d)+5d)

10=12-8d+5d

3d=2

d=\frac{2}{3}

Substitute the value of d into the first equation

6=u_{1}+4d

6=u_{1}+4(\frac{2}{3})

u_{1}=\frac{10}{3}

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