The explicit formula for the sequence is 3n -10
An arithmetic sequence is a series of terms which have common difference between its consecutive numbers.
The sequence given is
−7, −4, −1, 2, 5, …
The common difference between each term is d =3
-4-(-7) = 3
-1-(-4) =3
The nth term for a sequence is given by
[tex]\rm T_n = a +(n-1)d[/tex]
Here a is the first term = -7
n is the no. of terms = n
d is the common difference = 3
Therefore the equation will be
[tex]\rm T _n = -7 + (n-1) * 3[/tex]
[tex]\rm T _n[/tex] = -7 +3n -3
[tex]\rm T _n[/tex] = 3n -10
Therefore the explicit formula for the sequence is 3n -10 .
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