SOLUTION: Given the sequence 4;X-2;32... 1.1 Which term of the sequence is 158?

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Question 1023888: Given the sequence 4;X-2;32...
1.1 Which term of the sequence is 158?

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Given the sequence 4,x-2,32,............,a%5Bn%5D
first find x using common difference rule:
d=%28x-2%29-4=x-6...eq.1
d=32-%28x-2%29=32-x%2B2=34-x.....eq.2
from eq.1 and eq.2 we have:
x-6=34-x
2x=34%2B6
2x=40
x=20
so, your sequence is:
4,%2820-2%29,32,............,a%5Bn%5D or 4,18,32,............,a%5Bn%5D
the common difference is d=x-6=20-6=14
to find any term of an arithmetic sequence:
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d where a%5B1%5D is the first term of the sequence, d is the common difference, n is the number of the term to find.
your formula will be:
a%5Bn%5D=4%2B14%28n-1%29 for n=1,2,3,.........
if a%5Bn%5D=158, then
158=4%2B14%28n-1%29
158-4=14%28n-1%29
154%2F14=n-1
11=n-1
n=11%2B1
n=12
n=36
so, 12th element of your sequence is 158