Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest
hundredth.
-$$a _ { 5 } = 15 , a _ { 21 } = 95$$
A) $a _ { 1 } = 80 , d = 5$
B) $\mathrm { a } _ { 1 } = 80 , \mathrm {~d} = - 5$
C) $a _ { 1 } = - 5 , d = 5$
D) $a _ { 1 } = - 5 , d = 80$

Question

Quizplus · Accepted Answer

Given two terms of an arithmetic sequence, $a_5 = 15$ and $a_{21} = 95$, we can use the formula for the $n$th term of an arithmetic sequence, $a_n = a_1 + (n - 1)d$, where $a_1$ is the first term and $d$ is the common difference. Substituting the given values into the formula for both terms allows us to set up a system of equations to solve for $a_1$ and $d$. Solving this system yields $a_1 = -5$ and $d = 5$, making option C correct.

Find the First Term and the Common Difference for the Arithmetic