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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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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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