# Log + Sequence Test

Name:________________________

Let Sn be the sum of the first n terms of an arithmetic sequence, whose first three terms are u1, u2 and u3. It is known that S1 = 7, and S2 = 18. (a) (b) (c) Write down u1. Calculate the common difference of the sequence. Calculate u4. (Total 6 marks)

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2.

A theatre has 20 rows of seats. There are 15 seats in the first row, 17 seats in the second row, and each successive row of seats has two more seats in it than the previous row. (a) (b) Calculate the number of seats in the 20th row. Calculate the total number of seats. (Total 6 marks)

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3.

Gwendolyn added the multiples of 3, from 3 to 3750 and found that 3 + 6 + 9 + … + 3750 = s. Calculate s. (Total 6 marks)

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*4.

Find the term containing x10 in the expansion of (5 + 2x2)7. (Total 6 marks)

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*5.

Use the binomial theorem to complete this expansion. (3x +2y)4 = 81x4 + 216x3 y +... (Total 4 marks)

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6.

(a) (b)

Given that log3x – log3(x – 5) = log3A, express A in terms of x. Hence or otherwise, solve the equation log3x – log3(x – 5) = 1. (Total 6 marks)

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7.

Find the exact solution of the equation 92x = 27(1–x).

(Total 6 marks)

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*8.

If loga 2 = x and loga 5 = y, find in terms of x and y, expressions for (a) (b) log2 5; loga 20. (Total 4 marks)

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9.

Solve the equation log9 81 + log9

+ log9 3 = log9 x.

(Total 4 marks)

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