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##### Find the Nth Term Using Algebraic Expression

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6,10,14,18,22,...

Oct 18th, 2017

 Given the sequence 6,10,14,18,…… a) Find the nth term b) the 20th term c)If the nth term is 42, what is the value of n?

We look at the differences between each term
6 10 14 18
\ _/\_ /\_ /
4 4 4
The difference is four
The general formula for the nth term is:
 nth term = a + (n-1)d
where a = the first term =6
n = the number of the term
D = the difference = 4
For this sequencenth term = 6 + (n-1)4
= 6 + 4n - 4
= 2 + 4n
We can now use this formula to work out the value of any term in the sequence.
b)20th term =
2 + 4 x 20
= 82
because n = 20
c)nth term = 42
42 = 2 + 4n
40 = 4n
n = 10

So the 10th term is 42.

This formula will work for any linear sequence. In a linear sequence the difference is constant. 4 in the sequence above.

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