Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence.
-2, 10, 18, 26, 34, . . .
A) $a _ { n } = 2 ( 4 n - 3 ) ; a _ { 6 } = 42$
B) $a _ { n } = 8 n - 3 ; a _ { 6 } = 45$
C) $a _ { n } = 6 n - 8 ; a _ { 6 } = 28$
D) $a _ { n } = 2 ( 8 ) ^ { n - 1 } ; a _ { 6 } = 16$

Question

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence.
-2, 10, 18, 26, 34, . . . 
A) $a _ { n } = 2 ( 4 n - 3 ) ; a _ { 6 } = 42$
B) $a _ { n } = 8 n - 3 ; a _ { 6 } = 45$
C) $a _ { n } = 6 n - 8 ; a _ { 6 } = 28$
D) $a _ { n } = 2 ( 8 ) ^ { n - 1 } ; a _ { 6 } = 16$

Quizplus · Accepted Answer

The sequence is arithmetic with a common difference of 8. The first term $a_1 = 2$. 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 $a_1 = 2$ and $d = 8$ gives $a_n = 2 + (n - 1)8 = 2 + 8n - 8 = 8n - 6$, which simplifies to $2(4n - 3)$. For $a_6$, substituting $n = 6$ into the formula gives $a_6 = 2(4(6) - 3) = 2(24 - 3) = 2(21) = 42$.

Find an and a6a _ { n } \text { and } a _ { 6 }an​ and a6​

Find $a _ { n } \text { and } a _ { 6 }$