# Welcome to Physics and Maths.co.uk

01752 872809

## Physics and Maths Tuition and coaching for all - from GCSE through A-Level to Degree

## Now also coaching in GCSE/A-level Computer Science

### Proper, Improper and Mixed Fractions

### Fractional Arithmetic

### Changing the Subject of an Expression

### Multiplying Expressions

### Factorising Quadratic Expressions

### Solving Linear Equations

### Rationalising the Denominator

### Solving Simultaneous (Linear) Equations

### Solving Simultaneous Quadratic Equations

### 2 and 3 Part Ratios

### Completing the Square

### Sequences and Series

**Warning**: Division by zero in

**/home/physandm/public_html/php/class.exercise.php**on line

**800**

Ex. 0:

A geometric sequence has the following terms: u_{3}= 0.136, u

_{4}= -0.015, u

_{5}= 0.002, u

_{6}= -0.000, u

_{7}= 0.000, u

_{8}= -0.000, ...

Find the first term and the common ratio, and hence the sum to infinity (S

_{inf}) of the series.

[u

_{1}= 11.00, r = -0.11, S

_{inf}= 9.90]

Ex. 1:

A geometric sequence has the following terms: u_{3}= 0.111, u

_{4}= 0.037, u

_{5}= 0.012, u

_{6}= 0.004, u

_{7}= 0.001, u

_{8}= 0.000, ...

Find the first term and the common ratio, and hence the sum to infinity (S

_{inf}) of the series.

[u

_{1}= 1.00, r = 0.33, S

_{inf}= 1.50]

Ex. 2:

A geometric sequence has the following terms: u_{4}= 0.019, u

_{5}= 0.002, u

_{6}= 0.000, u

_{7}= 0.000, u

_{8}= 0.000, u

_{9}= 0.000, ...

Find the first term and the common ratio, and hence the sum to infinity (S

_{inf}) of the series.

[u

_{1}= 14.00, r = 0.11, S

_{inf}= 15.75]

Ex. 3:

A geometric sequence has the following terms: u_{5}= -0.012, u

_{6}= 0.003, u

_{7}= -0.001, u

_{8}= 0.000, u

_{9}= -0.000, u

_{10}= 0.000, ...

Find the first term and the common ratio, and hence the sum to infinity (S

_{inf}) of the series.

[u

_{1}= -3.00, r = -0.25, S

_{inf}= -2.40]

Ex. 4:

A geometric sequence has the following terms: u_{5}= 0.235, u

_{6}= -0.078, u

_{7}= 0.026, u

_{8}= -0.009, u

_{9}= 0.003, u

_{10}= -0.001, ...

Find the first term and the common ratio, and hence the sum to infinity (S

_{inf}) of the series.

[u

_{1}= 19.00, r = -0.33, S

_{inf}= 14.25]

Ex. 5:

A sequence has the following terms: u_{3}= -0.31, u

_{4}= -0.05, u

_{5}= -0.01, u

_{6}= -0.00, u

_{7}= -0.00, u

_{8}= -0.00, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 12

^{th}term (a

_{12}).

[Geometric, u

_{1}= -11.00, r = 0.17, u

_{12}= -0.00]

Ex. 6:

A sequence has the following terms: u_{4}= 0.00, u

_{5}= -0.00, u

_{6}= 0.00, u

_{7}= -0.00, u

_{8}= 0.00, u

_{9}= -0.00, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 14

^{th}term (a

_{14}).

[Geometric, u

_{1}= -6.00, r = -0.03, u

_{14}= 0.00]

Ex. 7:

A sequence has the following terms: a_{10}= 176, a

_{11}= 192, a

_{12}= 208, a

_{13}= 224, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 62

^{th}term (a

_{62}).

[Arithmetic, a

_{1}= 16, d = 16, a

_{62}= 992]

Ex. 8:

A geometric sequence has the following terms: u_{3}= -8.000, u

_{4}= -8.000, u

_{5}= -8.000, u

_{6}= -8.000, u

_{7}= -8.000, u

_{8}= -8.000, ...

Find the first term and the common ratio, and hence the sum to infinity (S

_{inf}) of the series.

[u

_{1}= -8.00, r = 1.00, S

_{inf}= 0.00]

Ex. 9:

A geometric sequence has the following terms: u_{4}= 0.593, u

_{5}= 0.198, u

_{6}= 0.066, u

_{7}= 0.022, u

_{8}= 0.007, u

_{9}= 0.002, ...

Find the first term and the common ratio, and hence the sum to infinity (S

_{inf}) of the series.

[u

_{1}= 16.00, r = 0.33, S

_{inf}= 24.00]

### Polynomial Long Division

### Factor and Remainder Theorem

### Roots of a cubic

### Differentials

### Finding Turning Points

### Pythagorus

### Sine and Cosine Rules

### Vectors

Website by Quality Website Design