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- Question 1 of 10
##### 1. Question

A sequence is defined by \({u_n} = 7n – 3\). Find the largest term of the sequence that is smaller than \(1000\).

CorrectIncorrect - Question 2 of 10
##### 2. Question

If \({u_{10}} = 100\) and \({u_{15}} = 175\), find \({u_{100}}\) of the arithmetic sequence.

CorrectIncorrect - Question 3 of 10
##### 3. Question

Find the sum of multiples of 9 between 26 and 1000.

Sum =

CorrectIncorrect##### Hint

\({S_n} = \dfrac{n}{2}\left[ {2{u_1} + \left( {n – 1} \right)d} \right]\) or \({S_n} = \dfrac{n}{2}\left( {\text{first term} + \text{last term}} \right)\)

- Question 4 of 10
##### 4. Question

\(k,3k\) and \(20 – k\) are consecutive terms of a geometric sequence. Find the integral value of \(k \).

\( k = \)

CorrectIncorrect - Question 5 of 10
##### 5. Question

Consider the geometric sequence $k + 3,k,4, \cdots $. Find the positive value of \(k \).

\(k = \)

CorrectIncorrect##### Hint

\({T_n} = {u_1}{r^{n – 1}}\)

- Question 6 of 10
##### 6. Question

Consider the sequence \(6,12,18, \cdots \). Find the number of terms between \(1000\) and \(10 000\).

Number of terms is

CorrectIncorrect##### Hint

\({a^x} = y \Rightarrow x = {\log _x}y\)

- Question 7 of 10
##### 7. Question

Find the interest rate per annum, correcting to 2 decimal places, that would enable an investment of \($5000\) to grow to \($7000\) over 3 years if interest is compounded quarterly.

CorrectIncorrect##### Hint

\(A = P{\left( {1 + r} \right)^n}\)

- Question 8 of 10
##### 8. Question

The third term is 0.5 and the eighth term is 16. Find the sum of the first eight terms.

Sum of the first seven terms =

CorrectIncorrect##### Hint

\({S_n} = \dfrac{{{u_1}\left( {{r^n} – 1} \right)}}{{r – 1}}\)

- Question 9 of 10
##### 9. Question

Find the sum of all powers of 2 between 500 and 50000.

number of terms =

CorrectIncorrect##### Hint

\({S_n} = \dfrac{{{u_1}\left( {{r^n} – 1} \right)}}{{r – 1}}\)

- Question 10 of 10
##### 10. Question

Find the value of \(x \), if \(1 + 3x + 9{x^2} + \cdots = \dfrac{2}{3}\)

CorrectIncorrect##### Hint

\({S_\infty } = \dfrac{{{u_1}}}{{1 – r}}\)