Sequences

Here are the first five terms of an arithmetic sequence.

2   5   8   11   14

Write down an expression, in terms of , for the th term of this sequence.

Is 299 a term of this sequence?

You must give a reason for your answer.

Write down an expression, in terms of , for the th term of this sequence.

In all the following sequences, after the first two terms, the rule is to add the previous two terms to find the next term.

Write down the next two terms in this sequence.
   

1    2    3    5    8    13      ...........      ...........

Write down the first two terms of this sequence.

.............       .............   3    11    14

      2         10

[3]

      -33                18

[5]

An arithmetic series has first term 1 and common difference 4.

Find the sum of all terms of the series from the 41st term to the 100th term inclusive.

The sum of the first terms of an arithmetic series, , is 292
The 2nd term of is 8.5
The 5th term of is 13

Find the value of .
Show clear algebraic working.

...................................................... 

Mario is going to save $50 in the year 2021

He is going to continue to save, up to and including the year 2070, by increasing the amount he saves each year by 

Mario will save a total of $33 125 from 2021 to 2070

Work out the value of .

....................

The first term of an arithmetic series  is –6
The sum of the first 30 terms of is 2865

Find the 9th term of .

In an arithmetic series, the  term is 
In the same arithmetic series, the  term is 

Work out the sum of the first  terms of the arithmetic series.

Work out the sum of the multiples of  between  and 

Here are the first five terms of an arithmetic sequence.

Work out the sum of all the terms from the  term to the  term inclusive.

Theo starts with savings of £18
James starts with no savings.

Each week from now,

   Theo will save £4.50 and James will save £4

In how many weeks will Theo and James have savings in the ratio 15 : 8 ?

A sequence is defined using this term-to-term rule,

where and are constants.

Given that  ,  and , find the value of and the value of .

= ................

= .................

A sequence is defined by the rule 

If , calculate

=............................[3]

=............................[3]

Here are the first four terms of an arithmetic sequence.

3   10   17   24

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

Is 150 a term of this sequence?

You must explain how you get your answer.

Here are the first five terms of an arithmetic sequence.

2   6   10   14   18

Write down an expression, in terms of , for the th term of this sequence.

Is 86 a term in the sequence?

You must give a reason for your answer.

Here are the first four terms of an arithmetic sequence.

11   17   23   29

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

Is 121 a term of this arithmetic sequence?
You must explain your answer.

Here are the first four terms of an arithmetic sequence.

6   10   14   18

Write an expression, in terms of , for the th term of this sequence.

The th term of a different arithmetic sequence is 

Is 108 a term of this sequence?

Show how you get your answer.

Here are the first five terms of an arithmetic sequence.

4   9   14   19   24

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

Here are the first five terms of a different sequence.

2      2      0      -4      -10

An expression for the th term of this sequence is 

Write down, in terms of , an expression for the th term of a sequence whose first five terms are  

4      4      0      -8      -20

The  th term of a number sequence is ² + 1

Write down the first three terms of the sequence.

Here are the first four terms of a sequence of fractions.

The numerators of the fractions form the sequence of whole numbers 
The denominators of the fractions form the sequence of odd numbers 

Write down an expression, in terms of , for the  term of this sequence of fractions.

Here are the first five terms of an arithmetic sequence.

Find the sum of the first 100 terms of this sequence.

Here are the first four terms of an arithmetic sequence.

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

Write down an expression, in terms of , for the  term of this sequence.

Here are the first five terms of a number sequence .

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

The  term of a sequence  is given by 

There are numbers that are terms in both the sequence  and the sequence 

Find one of these numbers.

Here are the first five terms of a number sequence.

7    11    15    19    23

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

The th term of a different number sequence is given by 

Write down the first 3 terms of this sequence.

Yuen says there are no numbers that are in both of the sequences.

Yuen is correct.

Explain why.

A sunflower grows at a rate of 4 cm each day.

How many days does it take to grow from a height of 80 cm to more than 1.06 m?

If the sunflower grows at a faster rate, how would this affect your answer to part ()?

The nth term of an arithmetic series is  where for all

The sum to terms of the series is

Given that  and that 

find the value of

Here are the first four terms of an arithmetic series.

Given that the 15th term of the series is ,
calculate the sum of the first 30 terms of the series.

and  are three consecutive terms of an arithmetic sequence.

Prove that the common difference of the sequence is 

An arithmetic series has first term and common difference , where is a prime number.

The sum of the first n terms of the series is and

Find the value of and the value of
Show clear algebraic working.

The sum of the first 48 terms of an arithmetic series is 4 times the sum of the first 36 terms of the same series.

Find the sum of the first 30 terms of this series.

The 25th term of an arithmetic series is 44.5
The sum of the first 30 terms of this arithmetic series is 765

Find the 16th term of the arithmetic series.
Show your working clearly.

The  term of an arithmetic series, , is 
The sum of the first  terms of  is 

Find the  term of .
Show your working clearly.

The 3rd term of an arithmetic series, , is 19
The sum of the first 10 terms of is 290

Find the 10th term of .