Chapter 29

Determine the next two terms in the series: \(3,6,9,12, \ldots\)

Determine the next two terms in the series: \(2,6,18,54, \ldots\)

The \(n^{\prime}\) th term of a sequence is given by \(3 n+1\). Write down the first four terms.

The \(n^{\prime}\) th term of a series is given by \(4 n-1\). Write down the first four terms.

Find the \(n^{\prime}\) th term of the series: \(1,4,7, \ldots\)

Find the \(n\) 'th term of the sequence: \(3,9,15\), \(21, \ldots\). Hence determine the 15 th term of the series.

Find the \(n^{\prime}\) th term of the series: \(1,4,9\), \(16,25, \ldots\)

Determine (a) the ninth, and (b) the sixteenth term of the series \(2,7,12,17, \ldots .\)

The 6th term of an \(A P\) is 17 and the 13 th term is 38 . Determine the 19 th term.

Determine the number of the term whose value is 22 in the series \(2 \frac{1}{2}, 4,5 \frac{1}{2}, 7, \ldots\).

Find the sum of the first 12 terms of the series \(5,9,13,17, \ldots\)

Find the sum of the first 21 terms of the series \(3.5,4.1,4.7,5.3, \ldots\)

The sum of 7 terms of an \(A P\) is 35 and the common difference is \(1.2\). Determine the first term of the series.

Three numbers are in arithmetic progression. Their sum is 15 and their product is 80 . Determine the three numbers.

Find the sum of all the numbers between 0 and 207 which are exactly divisible by 3 .

The first, twelfth and last term of an arithmetic progression are \(4,31 \frac{1}{2}\), and \(376 \frac{1}{2}\) respectively. Determine (a) the number of terms in the series, (b) the sum of all the terms and (c) the 80 'th term.

Determine the tenth term of the series 3,6, \(12,24, \ldots\)

Find the sum of the first 7 terms of the series, \(\frac{1}{2}, 1 \frac{1}{2}, 4 \frac{1}{2}, 13 \frac{1}{2}, \ldots\)

Which term of the series \(2187,729,243, \ldots\) is \(\frac{1}{4} ?\)

Find the sum of the first 9 terms of the series \(72.0,57.6,46.08, \ldots\)

In a geometric progression the sixth term is 8 times the third term and the sum of the seventh and eighth terms is 192 . Determine (a) the common ratio, (b) the first term, and (c) the sum of the fifth to eleventh terms, inclusive.

A hire tool firm finds that their net return from hiring tools is decreasing by \(10 \%\) per annum. If their net gain on a certain tool this year is \(£ 400\), find the possible total of all future profits from this tool (assuming the tool. lasts for ever).

Problem 26. If \(£ 100\) is invested at compound interest of \(8 \%\) per annum, determine (a) the value after 10 years,(b) the time, correct to the nearest year, it takes to reach more than \(£ 300\).

A drilling machine is to have 6 speeds ranging from \(50 \mathrm{rev} / \mathrm{min}\) to \(750 \mathrm{rev} / \mathrm{min}\). If the speeds form a geometric progression determine their values, each correct to the nearest whole number.