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

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

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

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

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

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

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.

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

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

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