Engineering and Science Admissions Test

ESAT Maths 1 Sequences & series questions

1 original ESAT Maths 1 sequences & series questions in the real exam style, each with a step-by-step worked solution and an explanation of why the tempting wrong answers are wrong. Try each one before opening the solution.

Methods on this page: Quadratic sequences: second differences give the n² term

Question 1ESAT Maths 1Standard

The first five terms of a quadratic sequence are

-3, 3, 15, 33, 57

. What is the 20th term?

A $111$
B $1137$
C $1138$
D $1143$
E $1257$

Show the answer and worked solution

Answer: B · Method: Quadratic sequences: second differences give the n² term

The second difference is $6$ , so the $n^2$ coefficient is $6 \div 2 = 3$ .
Subtracting $3n^2$ leaves a linear sequence, giving $u_n = 3n^2 - 3n - 3$ .
So $u_{20} = 1137$ .

Why the tempting wrong answers are wrong

A: The first differences aren't constant, so it isn't a linear sequence.
E: That's the 21th term.

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ESAT Maths 1 Sequences & series questions

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