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!
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