Find a general term an for the sequence whose first four terms are given.
-$1,4,7,10 , \ldots$
A) $a _ { n } = n + 3$
B) $a _ { n } = 1 ( 3 ) ^ { n - 1 }$
C) $a _ { n } = 3 n - 2$
D) $a _ { n } = 2 n - 3$

Question

Quizplus · Accepted Answer

The sequence increases by 3 each time (4-1=3, 7-4=3, 10-7=3), so it's an arithmetic sequence with a common difference of 3. The first term $a_1 = 1$. The formula for the $n$th term of an arithmetic sequence is $a_n = a_1 + (n - 1)d$, where $d$ is the common difference. Substituting $a_1 = 1$ and $d = 3$ gives $a_n = 1 + (n - 1)3 = 3n - 2$.

Find a General Term an for the Sequence Whose First 1,4,7,10,…1,4,7,10 , \ldots1,4,7,10,…

Find a General Term an for the Sequence Whose First $1,4,7,10 , \ldots$