Sequences Practice Questions

The first term of a sequence is $7$.

The term-to-term rule for this sequence is multiply by 2 then subtract 5

Work out the next three terms of the sequence.

The $n$th term of a different sequence is $n^2 + 3n$

Write down the first three terms of this sequence.

Here are the first four terms of a sequence of triangular numbers.

$1 \quad 3 \quad 6 \quad 10$

Write down the next two terms of this sequence.

The first two terms of a Fibonacci-type sequence are $4$ and $7$

Each term after the first two terms is the sum of the two previous terms.

Write down the first five terms of this sequence.

Find an expression, in terms of $n$, for the $n$th term of this sequence.

Work out the 50th term of this sequence.

Find an expression, in terms of $n$, for the $n$th term of this sequence.

Ravi says,

"245 is a term of this sequence."

Is Ravi correct?
You must show how you get your answer.

Find an expression, in terms of $n$, for the $n$th term of this sequence.

$245$ is a term of this sequence.

Work out which term of the sequence $245$ is.

Write down the common ratio of this sequence.

Write down the next two terms of this sequence.

Work out the first term of this sequence that is less than $1$

You must show all your working.

The $n$th term of a sequence is given by $an^2 + bn + 4$, where $a$ and $b$ are integers.

The 1st term of the sequence is $7$

The 3rd term of the sequence is $25$

Find the 10th term of the sequence.

Show that the common ratio of the sequence is $\sqrt{3}$

Find the 6th term of the sequence.
Give your answer in the form $a\sqrt{3}$, where $a$ is an integer.

Work out the number of grey tiles in Pattern 10

Show that the total number of tiles in Pattern $n$ is $(n+2)^2$

One pattern in this sequence is made from a total of $225$ tiles.

Work out the number of grey tiles in this pattern.