Find a formula for a_n for the arithmetic sequence. a₃ = 94, a₆ = 87 A)a_n = $\frac { 7 } { 3 }$ n - 101 B)a_n = $- \frac { 7 } { 3 }$ n + 101 C)a_n = 101 - 303n D)a_n = $\frac { 7 } { 3 }$ n + 303 E)a_n = 101 + 303n

Question

Quizplus · Accepted Answer

The correct formula for the arithmetic sequence given the terms $a_{13} = 94$ and $a_{16} = 87$ is found by first determining the common difference $d$. Since the sequence decreases from $a_{13}$ to $a_{16}$, $d = \frac{87 - 94}{16 - 13} = \frac{-7}{3}$. Using the formula for an arithmetic sequence $a_n = a_1 + (n - 1)d$, and substituting $n = 13$ and $a_{13} = 94$, we can solve for $a_1$. Rearranging the formula gives $a_1 = a_n - (n - 1)d$, thus $a_1 = 94 - (13 - 1)(-\frac{7}{3}) = 101$. Therefore, the formula for the nth term is $a_n = 101 - \frac{7}{3}n$, which matches choice B.

Find a Formula for An for the Arithmetic Sequence 73\frac { 7 } { 3 }37​

Find a Formula for A_n for the Arithmetic Sequence $\frac { 7 } { 3 }$