What I learned

Before winter break for lesson 10.2, I have learnt about arithmetic sequences.

Arithmetic Sequence

An arithmetic sequence is one of the different types of sequences. It has a commom difference that is added (addition) to the previous term each time. An arithmetic sequence makes a straight line unlike a geometic sequence.

Formula for the General Term

The formula for the general term of an arithmetic sequence is:

tn = t1 + (n – 1)d

so, general term = term 1 + (position of term – 1) multiplied by commom difference

Examples

Ex. 2, 12, 22, 32, 42… What is the general term? The 50th term?

t1 = 2       d = 10

tn = 2 + (n – 1)10

tn = 2 + 10n – 10

tn = 10n – 8

 

t50 = 10(50) – 8

t50 = 500 – 8

t50 – 492

 

Ex. How many terms in the sequence 3, -1, -5 … -117

t1 = 3         d = -4

tn = 3 + (n – 1)-4

tn = 3 – 4n +4

tn = -4n + 7

 

-117 = -4n + 7

-7              -7

-124 = -4n

÷-4     ÷-4

31 = n

 

Ex. If t2 = 10 and t6 = 34, determine t1 and the general term.

t2 + 4d = t6

10 + 4d = 34

-10           -10

4d = 24

÷4    ÷4

d = 6

 

t1 = t2 – d

t1 = 10 – 6

t1 = 4

 

tn = 4 + (n – 1)6

tn = 4 + 6n – 6

tn = 6n – 2

 

And that is what I have learnt before winter break!