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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

6-2=4, so d=4

u_{1}=2

Substitute into the arithmetic sequence formula:

u_{203}=2+(203-1)(4)

u_{203}=2+(202)(4)

u_{203}=2+808

u_{203}=810



b) Solve algebraically using the same formula:

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

3174=2+(n-1)(4)

3172=(n-1)(4)

793=n-1

n=794

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