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a) Use the arithmetic sequence formula:

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

d is an unknown variable

Find d by subtracting two consecutive terms

11-3=8, so d=8

u_{1}=3

Substitute into the arithmetic sequence formula:

u_{107}=3+(107-1)(8)

u_{107}=3+(106)(8)

u_{107}=3+848

u_{107}=851



b) Solve algebraically using the same formula:

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

659=3+(n-1)(8)

656=(n-1)(8)

82=n-1

n=83

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