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Trava [24]
3 years ago
13

1st term in sequence is 6-4th term is -6, the 8th term is -22 write a function that can be used to find the nth term of the sequ

ence
Mathematics
2 answers:
Gemiola [76]3 years ago
8 0

a_{n} = 10 - 4n

this is an arithmetic sequence with n th term

a_{n} = a_{1} + (n - 1 )d

where a_{1} is the first term and d the common difference

given a_{4} = - 6, then

6 + 3d = - 6 ( subtract 6 from both sides )

3d = - 12 ( divide both sides by 3 )

d = - 4 ← common difference hence

a_{n} = 6 - 4 (n - 1 ) = 6 - 4n + 4 = 10 - 4n


laila [671]3 years ago
4 0

EXPLANATION


The nth term of the sequence is given by


U_n=a+(n-1)d


Where

a


is the first term and



d



is the constant difference.


We were given that,


a=6


S we just need the common difference to write the nth term.


We can get that from another information given to us.


We were also given that the 4th term is 6. This gives the equation.


a+3d=-6



We substitute

a=6


to obtain




6+3d=-6


Or




2+d=-2


This implies,



d=-2-2


d=-4



We substitute these values into the general formula to obtain,



U_n=6+(n-1)\times-4


This gives us,



U_n=6+-4n+4





U_n=10-4n



Hence the nth term of the sequence is,



10-4n

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