Find a formula for a_n?for the arithmetic sequence. ? A₁ = -5,a₅ = 18 ?

Question

Quizplus · Accepted Answer

The formula for an arithmetic sequence is $a_n = a_1 + (n-1)d$, where $a_n$ is the nth term, $a_1$ is the first term, and $d$ is the common difference. Given $a_1 = -5$ and $a_5 = 18$, we can find $d$ by using the formula for the 5th term: $18 = -5 + (5-1)d$, solving this gives $d = \frac{23}{4}$. Substituting $a_1 = -5$ and $d = \frac{23}{4}$ into the general formula gives $a_n = -5 + (n-1)\frac{23}{4}$, which simplifies to $a_n = \frac{23}{4}n - \frac{43}{4}$.

Find a Formula for An ?for the Arithmetic Sequence 234\frac { 23 } { 4 }423​

Find a Formula for A_n?for the Arithmetic Sequence $\frac { 23 } { 4 }$