Question 1

The $n$th term of a sequence is $8n+3$.

Which term in the sequence is 51?

Accepted Answer

$6$th term

Answer

$10$th term

Answer

$4$th term

Answer

$8$th term

Question 2

The $n$th term of a sequence is $8n+3$.

Work out the first number in the sequence to exceed 100

Accepted Answer

$107$

Answer

$101$

Answer

$104$

Answer

$111$

Question 3

The $n$th term of a sequence is $n^2-30$.

Work out the 4th number in the sequence.

Accepted Answer

$-14$

Answer

$4$

Answer

$-8$

Answer

$12$

Question 4

A Fibonacci sequence starts $m, n, m+n, ...$

Write an algebraic expression for the seventh term in the sequence.

Accepted Answer

$5m+8n$

Answer

$7m+7n$

Answer

$3m+9n$

Answer

$4m+7n$

Question 5

A Fibonacci sequence starts $m, n, m+n...$

If the first term in the sequence is $3$ and the difference between the first and third terms is $5$, work out the value of the eighth term in the sequence.

Accepted Answer

$89$

Answer

$53$

Answer

$77$

Answer

$66$

Question 6

An arithmetic sequence has first term 5 and third term 11.

What is the $n$th term of the sequence?

Accepted Answer

$3n+2$

Answer

$5n+1$

Answer

$2n+3$

Answer

$n+4$

Question 7

Use your calculator to work out the sum of the 50th and 60th terms in the sequence that starts $12, 9, 6, 3, ...$

Accepted Answer

$-300$

Answer

$-340$

Answer

$-240$

Answer

$-180$

Question 8

Gloria’s salary in her new job is $£24 000$ in the first year. Every year she gets a pay rise so that her annual salaries form an arithmetic sequence. When her annual salary reaches $£27 000$ she gets no further pay rises. In her fourth year she is paid $£24 900$.

In what year does she reach her maximum salary?

Accepted Answer

11th year

Answer

14th year

Answer

8th year

Answer

5th year

Question 9

Here is a number sequence: $3, \frac{5}{2},  \frac{7}{3},  \frac{9}{4},  \frac{11}{5},...$

Work out an expression for the $n$th term of the sequence.

Accepted Answer

$\frac{ 2n+1 }{ n }$

Answer

$4n+1$

Answer

$\frac{ n+5}{ 2 }$

Answer

$3n-4$

Question 10

What is the $n$th term of the sequence $3, 12, 27,48,...$?

Accepted Answer

$3n^2$

Answer

$n^2 +3$

Answer

$\frac{ n^2 }{ 3 }$

Answer

$n^2 -3$

Question 11

Work out the next two terms in the sequence: $5, 8, 13, 20,...$

Accepted Answer

$29$ and $40$

Answer

$22$ and $33$

Answer

$33$ and $38$

Answer

$25$ and $29$

Question 12

Work out the next two terms in the sequence: $-2, 5, 14, 25,...$

Accepted Answer

$38$ and $53$

Answer

$30$ and $41$

Answer

$42$ and $60$

Answer

$35$ and $49$

Question 13

A sequence has $n$th term $n^2 + 2n + 2$.

Work out which term in the sequence has a value of $50$.

Accepted Answer

6th term

Answer

14th term

Answer

17th term

Answer

10th term

Question 14

Work out the $n$th term of the sequence: $10, 12, 16, 22, ...$

Accepted Answer

$n^2 − n + 10$

Answer

$2n^2 + 10$

Answer

$4n^2 − 3n + 2$

Answer

$4n + 6$

Question 15

Work out the $n$th term of the sequence: $-9, 2, 17, 36,...$

Accepted Answer

$2n^2 + 5n − 16$

Answer

$3n^2 +6n $

Answer

$3n^2 +12 $

Answer

$n^2 - 2n +12$

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