4.2 Arithmetic Sequences & Series

The first two terms in an arithmetic sequence are  and 3.  The fourth term is .

Find the value of .

An arithmetic sequence has first term  and common difference , where .  The fourth term in the sequence is 4.

Find the value of , giving your answer as an exact value.

The third term of an arithmetic series is 32.  The eleventh term is 0.  The sum of the first  terms is -44.

Find the value of .

The sum of the first twelve terms in an arithmetic series is 654.  The sum of the first twenty terms in the same series is 530.  Find the 21^st term.

Prove that the sum of the first  odd numbers is a square number for any value of .

An arithmetic series is defined by

where  is an integer.

In terms of , find an expression for the number of terms in this series.

In addition to being an integer, what other two conditions must  satisfy for this to be a valid arithmetic series?

Show that the sum of this series is  .

The seventh term of an arithmetic series is , where  is a constant, and the sum of the first nine terms of the series is .

In terms of , find expressions for the first term and common difference of the series.

Given that the nineteenth term of the sequence is 57, find the sum of the first 25 terms of the series.

An arithmetic series is defined by

Find an expression for  in terms of  and 

For a particular value of ,   and .

Find the value of .

The first three terms in an arithmetic sequence are 

Find the possible values of .

An arithmetic sequence has first term  and common difference , where .  The fifth term of the sequence is 85.

Find:

the value of 

The third term of an arithmetic series is 2.  The twelfth term is 65.  The sum of the first  terms is 390.

Show that  .

Hence find the value of .

The sum of the first ten terms in an arithmetic series is 40.  The sum of the first twenty terms in the same series is 280.  Find the first term, , and the common difference, , of the series.

The sum of the first  terms of an arithmetic series is

Show that  .

Hence show that the sum of the first  terms is  .

Given that , find the value of .

The fifth term of an arithmetic series is , where  is a constant, and the sum of the first eight terms of the series is .

Show that the first term, , of the series is .

Find an expression for the common difference, , of the series in terms of .

Given that the ninth term of the sequence is 14, calculate:

the value of 

The sum of the first 30 terms of the series.

Calculate the sum of all the odd numbers between 0 and 150,

An arithmetic series is defined by

where  is an integer and a positive factor of 360.

In terms of , find an expression for the number of terms in this series.

Show that the sum of this series is  .

In terms of , find the 100th term of the arithmetic sequence defined by

Give your answer in simplest form.

The first three terms in an arithmetic sequence are  

Given that the first three terms in the sequence are all positive, find the fortieth term in the sequence.

The th term of an arithmetic series is 0.  The sum of the first  terms is also 0.

 Find the value of  in terms of  , giving clear reasons for your answer.

The sum of the first 20 terms in an arithmetic series is 290.  The sum of the first 24 terms in the same series is -180.  In general, the sum of the first   terms is .  Find the greatest value attained by  for any .

The sum of the first 24 terms in an arithmetic series is nine times the sum of the first two terms in the series. 

Find the sum of the first 90 terms in the series.