ESAT (Engineering and Science Admissions Test) · Mathematics 2

Sequences and series

9 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.

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A geometric series has first term $12$ and common ratio $\frac{1}{3}$ . What is its sum to infinity?
Evaluate $r = 1 \sum 10 (3 r - 2)$ .
What is the coefficient of $x^{2}$ in the expansion of $(2 - 3 x)^{4}$ ?
The first term of a geometric sequence is $4$ and the third term is $36$ , with all terms positive. What is the 5th term?
An arithmetic sequence has 5th term $17$ and 12th term $38$ . What is the sum of its first $20$ terms?
A geometric sequence has first term $3$ and common ratio $2$ . What is the smallest $n$ such that the sum of the first $n$ terms exceeds $1000$ ?
What is the coefficient of $x^{3}$ in the expansion of $(1 + 2 x)^{6}$ ?
A sequence is defined by $u_{1} = 5$ and $u_{n + 1} = 2 u_{n} - 3$ . What is $u_{5}$ ?
What is the sum of all positive multiples of $7$ that are less than $200$ ?

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