Answer:
Step-by-step explanation:
[tex]a_1=12\\a_2=15\\\\d=a_2-a_1=15-12=3\\\\a_n=a_1+d(n-1)\\\\a_n=12+3(n-1)\\a_n=12+3n-3\\a_n=3n+9[/tex]
Equation of the nth term of the given arithmetic sequence is equals to
aₙ = 3n +9.
" Arithmetic sequence is a sequence in which difference between two consecutive terms remain constant. "
Formula used
nth term in Arithmetic sequence
aₙ = a₁ + (n -1)d
Where
aₙ=nth term of the sequence
a₁ = first term of the sequence
n = number of terms
d = common difference
According to the question,
Given arithmetic sequence is
12, 15, 18, 21, ......
a₁ = 12
d = 15 - 12
= 3
Substitute the values in the formula of nth term we have,
aₙ = 12 + (n - 1) 3
⇒ aₙ= 12 + 3n -3
⇒ aₙ= 3n +9
Hence, equation of the nth term of the given arithmetic sequence is equals to aₙ = 3n +9.
Learn more about arithmetic sequence here
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