Write an equation for the $n$n th term of the arithmetic sequence. Then find $a_{30}$a30 .$-9,-6,-3,0,\ ...$−9,−6,−3,0, ...$a_n=$an= $a_{30}=$a30=
Question
Write an equation for the th term of the arithmetic sequence. Then find .
Sequence: (-9, -6, -3, 0, ...**
Equation:
Find:
Solution
The general formula for the nth term of an arithmetic sequence is given by:
a_n = a_1 + (n - 1) * d
where: a_n is the nth term a_1 is the first term d is the common difference
In this case, the first term a_1 is -9 and the common difference d is -6 - (-9) = 3.
So, the nth term of the sequence is given by:
a_n = -9 + (n - 1) * 3
Simplify this to:
a_n = -9 + 3n - 3 a_n = 3n - 12
To find the 30th term a_30, substitute n = 30 into the equation:
a_30 = 3*30 - 12 a_30 = 90 - 12 a_30 = 78
So, the 30th term of the sequence is 78.
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