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

\( k = \)

Correct

Incorrect

Question 5 of 10

5. Question

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

\(k = \)

Correct

Incorrect

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

Correct

Incorrect

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.

Correct

Incorrect

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.