Cambridge A-Level · Mathematics

Sequences and series

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

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

All 23 questions

The first term of an arithmetic progression is $4$ and its common difference is $6$ . What is the sum of its first $16$ terms?
The first term of an arithmetic progression is $7$ and its common difference is $5$ . What is the sum of its first $8$ terms?
The first term of an arithmetic progression is $9$ and its common difference is $4$ . What is the sum of its first $18$ terms?
The first term of an arithmetic progression is $6$ and its common difference is $6$ . What is the sum of its first $12$ terms?
The first term of an arithmetic progression is $4$ and its common difference is $5$ . What is the sum of its first $18$ terms?
The first term of an arithmetic progression is $4$ and its common difference is $6$ . What is the sum of its first $8$ terms?
What is the sum to infinity of the geometric series $6 + 3 + 3/2 + \dots$ ?
What is the sum to infinity of the geometric series $8 + 4 + 2 + \dots$ ?
The first term of an arithmetic progression is $7$ and its common difference is $3$ . What is the sum of its first $13$ terms?
The first term of an arithmetic progression is $8$ and its common difference is $3$ . What is the sum of its first $19$ terms?
The first term of an arithmetic progression is $3$ and its common difference is $3$ . What is the sum of its first $16$ terms?
The first term of an arithmetic progression is $3$ and its common difference is $5$ . What is the sum of its first $19$ terms?
The first term of an arithmetic progression is $3$ and its common difference is $6$ . What is the sum of its first $13$ terms?
What is the sum to infinity of the geometric series $4 + 8/3 + 16/9 + \dots$ ?
A geometric sequence has first term $5$ and common ratio $1.1$ . What is the smallest value of $n$ for which the sum of the first $n$ terms exceeds $400$ ?
What is the coefficient of $x^{2}$ in the expansion of $(2 - x) (1 + 3 x)^{5}$ ?
What is the sum to infinity of the geometric series $6 + 3/2 + 3/8 + \dots$ ?
What is the sum to infinity of the geometric series $2 + 1/2 + 1/8 + \dots$ ?
What is the sum to infinity of the geometric series $3 + 3/4 + 3/16 + \dots$ ?
What is the sum to infinity of the geometric series $2 + 1 + 1/2 + \dots$ ?
The first term of an arithmetic progression is $7$ and its common difference is $2$ . What is the sum of its first $16$ terms?
What is the sum to infinity of the geometric series $6 + 2 + 2/3 + \dots$ ?
What is the sum to infinity of the geometric series $3 + 3/2 + 3/4 + \dots$ ?

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