Arithmetic sequences and series

The first 3 terms of an arithmetic series are

(2x + 5) (3y – 4) (4x – 2)

where x and y are constants.

The sum of the first 9 terms of the series is 216

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

An arithmetic series has 30 terms.

The first term is a The common difference is d

The 20th term is 123 The sum of the 30 terms is 2880

Work out the value of a and the value of d Show clear algebraic working.

Here are the first three terms of an arithmetic sequence.

Find, as an integer, the sum of the first 40 terms of the sequence. Show clear algebraic working.

24A polygon has n sides, where n 5

The interior angles of the polygon form an arithmetic sequence.

The smallest angle of the polygon is 84° The common difference of the sequence is 4°

Work out the sum of the interior angles of the polygon. Show clear algebraic working.

Here are the first 4 terms in an arithmetic sequence.

3 7 11 15

The last term of the sequence is x The sum of the terms of the sequence is 7260

Find the value of x Show clear algebraic working.

The sum of the first 80 terms of an arithmetic series, S, is 470

The 75th term of S is 14.5

The sum of the first X terms of S is 171

Work out the value of X Show your working clearly.

22The first term of an arithmetic series is (2t + 1) where t 0 The n th term of this arithmetic series is (14 t – 5)

The common difference of the series is 3

The sum of the first n terms of the series can be written as p(qt – 1)^r where p, q and r are integers.

Find the value of p, the value of q and the value of r Show clear algebraic working.

p =_........ q =_........ r =_........

An arithmetic sequence has first term 8 and common difference 11 The sequence has k terms, where k 21

The sum of the last 20 terms of the sequence is 10 170

Find the value of k Show clear algebraic working.

23A polygon has n sides, where n 5

When arranged in order of size, starting with the largest number, the sizes of the interior angles of the polygon, in degrees, are the terms of an arithmetic sequence.

Here are the first five terms of this sequence.

177 175 173 171 169

Find the value of n Show clear algebraic working.

The sum of the first 10 terms of an arithmetic series is 4 times the sum of the first 5 terms of the same series.

The 8th term of this series is 45

Find the first term of this series. Show clear algebraic working.

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

The sum of the first n terms of the series is S_n and S_m = 39 S_2m = 320 Find the value of d and the value of m Show clear algebraic working.

An arithmetic series has first term a and common difference d.

The sum of the first 2n terms of the series is four times the sum of the first n terms of the series.

Find an expression for a in terms of d. Show your working clearly.

In an arithmetic series, the 6th term is 39 In the same arithmetic series, the 19th term is 7.8

Work out the sum of the first 25 terms of the arithmetic series.

Here are the first five terms of an arithmetic sequence.

8 15 22 29 36

Work out the sum of all the terms from the 50th term to the 100th term inclusive.

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

Find the 9th term of S.

Here are the first five terms of an arithmetic sequence.

7 10 13 16 19

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

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.

Work out the sum of the multiples of 3 between 1 and 1000

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.