Math help! *arithmetic sequenece* how do you write the first five term? :3
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# Math help! *arithmetic sequenece* how do you write the first five term? :3

[From: ] [author: ] [Date: 11-05-20] [Hit: ]
2,6,10,14.........
a(8)=26 a(12)=42

-2,2,6,10,14....

how did that work out?
*the numbers in (x) are under the a's like a exponent/power to thing but underneath if that made sense?? :S like a mini number yeah?

anywho I dont know how do this when I dont the difference or something.

help would be much appericated! :)

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An arithmetic sequence can be defined by a(n) = a + (n - 1)d.

First we plug the first term, a(8) = 26, into the formula:
26 = a + (8 - 1)d
26 = a + 7d
a + 7d = 26

Now we plug the second term, a(12) = 42, into the formula:
42 = a + (12 - 1)d
42 = a + 11d
a + 11d = 42

We now have two simultaneous equations which can be solved:
(a + 11d) - (a + 7d) = 42 - 26
a + 11d - a - 7d = 42 - 26
4d = 16
d = 4
a + 7d = 26
a = 26 - 7d
a = 26 - 7(4)
a = 26 - 28
a = -2

Then going back the original formula, we plug in these values:
a(n) = -2 + 4(n - 1)
a(n) = -2 + 4n - 4
a(n) = 4n - 6

Now we find the first five terms by plugging in the term number:
a(1) = -2
a(2) = 2
a(3) = 6
a(4) = 10
a(5) = 14

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a(8) and a(12) are the eighth and twelfth terms of the sequence.

Between terms 8 and 12 there are 4 equal differences.

so, 4d = 42 - 26 = 16

=> d = 4

The eighth term is a + 7d = a + 28 = 26 => a = -2

i.e. the sequence is -2, 2, 6,.....

:)>

-
The progression is that each number is 4 more than the one before
The number in the bracket is which term we are talking about. So the a(8) means the eighth term is 26 and the twelfth term is 42.
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