Singapore GCE A-Level · H2 Mathematics

Sequences, series and expansions

36 practice questions, each with the answer and an explanation.

Practise Sequences, series and expansions now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 36 questions

An arithmetic progression has first term $5$ and common difference $4$ . Find the sum of the first 20 terms.
An arithmetic progression has first term $3$ and common difference $7$ . Find the sum of the first 15 terms.
An arithmetic progression has first term $10$ and common difference $- 3$ . Find the sum of the first 12 terms.
An arithmetic progression has first term $2$ and common difference $5$ . Find the sum of the first 25 terms.
An arithmetic progression has first term $8$ and common difference $6$ . Find the sum of the first 18 terms.
An arithmetic progression has first term $- 4$ and common difference $3$ . Find the sum of the first 30 terms.
A geometric progression has first term $12$ and common ratio $\frac{1}{2}$ . Find the sum to infinity.
A geometric progression has first term $18$ and common ratio $\frac{1}{3}$ . Find the sum to infinity.
A geometric progression has first term $20$ and common ratio $\frac{2}{5}$ . Find the sum to infinity.
A geometric progression has first term $9$ and common ratio $\frac{2}{3}$ . Find the sum to infinity.
A geometric progression has first term $16$ and common ratio $\frac{3}{4}$ . Find the sum to infinity.
A geometric progression has first term $30$ and common ratio $\frac{1}{6}$ . Find the sum to infinity.
The geometric series $1 + \frac{x}{2} + \frac{x ^{2}}{4} + \dots$ converges. Find the set of possible values of $x$ .
The geometric series $1 + \frac{x}{3} + \frac{x ^{2}}{9} + \dots$ converges. Find the set of possible values of $x$ .
The geometric series $1 + \frac{x}{4} + \frac{x ^{2}}{16} + \dots$ converges. Find the set of possible values of $x$ .
The geometric series $1 + \frac{x}{5} + \frac{x ^{2}}{25} + \dots$ converges. Find the set of possible values of $x$ .
The geometric series $1 + \frac{x}{6} + \frac{x ^{2}}{36} + \dots$ converges. Find the set of possible values of $x$ .
Find the value of $\sum_{r = 1}^{4} (2 r + 1)$ .
Find the value of $\sum_{r = 1}^{6} (2 r + 1)$ .
Find the value of $\sum_{r = 1}^{8} (2 r + 1)$ .
Find the value of $\sum_{r = 1}^{10} (2 r + 1)$ .
Find the value of $\sum_{r = 1}^{12} (2 r + 1)$ .
Using the method of differences, find the value of $\sum_{r = 1}^{3} \frac{1}{r ( r + 1 )}$ .
Using the method of differences, find the value of $\sum_{r = 1}^{5} \frac{1}{r ( r + 1 )}$ .
Using the method of differences, find the value of $\sum_{r = 1}^{9} \frac{1}{r ( r + 1 )}$ .
Using the method of differences, find the value of $\sum_{r = 1}^{19} \frac{1}{r ( r + 1 )}$ .
Using the method of differences, find the value of $\sum_{r = 1}^{99} \frac{1}{r ( r + 1 )}$ .
Find the coefficient of $x^{2}$ in the Maclaurin series of $e^{2 x}$ .
Find the coefficient of $x^{2}$ in the Maclaurin series of $e^{3 x}$ .
Find the coefficient of $x^{2}$ in the Maclaurin series of $e^{4 x}$ .
Find the coefficient of $x^{2}$ in the Maclaurin series of $e^{5 x}$ .
Find the coefficient of $x^{2}$ in the expansion of $(1 + x)^{6}$ .
Find the coefficient of $x^{2}$ in the expansion of $(1 + x)^{7}$ .
Find the coefficient of $x^{2}$ in the expansion of $(1 + x)^{8}$ .
Find the coefficient of $x^{3}$ in the expansion of $(1 + x)^{9}$ .
Find the coefficient of $x^{3}$ in the expansion of $(1 + x)^{10}$ .

Keep practising

Ready for the full Singapore GCE A-Level test?

Take a mock test Singapore GCE A-Level hub

Sequences, series and expansions

Practise Sequences, series and expansions now

All 36 questions

Keep practising

More Singapore GCE A-Level topics

Ready for the full Singapore GCE A-Level test?