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An arithmetic sequence has 2u6=S6=5, where S6 is the sum of the first 6 terms. Find the second term, u2, of the sequence.
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Consider the equation z2+(2+2i)z+10i−15=0, where z∈C.
Write down
the sum of the roots.
the product of the roots.
It is given that z2+(2+2i)z+10i−15=0 has a real root.
Find both roots of the equation.
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Solve for x and y in the following system of equations:
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Solve for x in the equation 15−3x=274−x, giving your answer in terms of ln3 and ln5.
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Solve the equation 4lnx=ln81−8.
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Solve the equation 154−3x=92x, giving your answer in terms of ln3 and ln5.
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An arithmetic sequence has u3=5 and u7=−7.
Find the common difference d and the first term u1 of the sequence.
Hence find u10.
Find S10.
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A geometric sequence has u3=3 and u6=98. Find S∞ for this sequence.
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Ella invests $500 in a savings account that earns 4% interest per annum, compounded quarterly.
Find an expression for the balance of Ella's savings after n years.
Calculate the value of Ella's savings after 12 years. Give your answer to the nearest dollar.
Ella wants to purchase a racing bike for $700.
Find the number of years after which her savings will be sufficient to purchase the bike.
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