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a) Find the difference by subtracting two consecutive terms

d=u_{2}-u_{1}

d=log_{a}(bc)-log_{a}(b)

Use logarithm rules to solve: Quotient Rule

d=log_{a}(\frac{bc}{b})

Cancel out b

d=log_{a}(c)



b) Use the sum of a arithmetic sequence formula:

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

Find d and u_{1} ; use n=12

d=log_{a}(c) , c=a^{5}

Substitute into expression

d=log_{a}(a^{5})

Cancel a

d=5

u_{1}=log_{a}(b) ; b=a^{3}

Substitute into expression

u_{1}=log_{a}(a^{3})

Cancel a

u_{1}=3

Substitute back into formula

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

S_{12}=\frac{12}{2}[2(3)+(12-1)5]

S_{12}=6(6+55)

S_{12}=6(61)

S_{12}=366

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