Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest
hundredth.
-$$a _ { 5 } = 112 , a _ { 34 } = 605$$
A) $a _ { 1 } = 493 , d = 44$
B) $a _ { 1 } = 493 , d = 17$
C) $\mathrm { a } _ { 1 } = 44 , \mathrm {~d} = 17$
D) $a _ { 1 } = 44 , d = 493$

Question

Quizplus · Accepted Answer

The formula for the nth term of 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 $a_5 = 112$ and $a_{34} = 605$, we can set up two equations: $112 = a_1 + 4d$ and $605 = a_1 + 33d$. Solving these equations simultaneously yields $a_1 = 44$ and $d = 17$.

Find the First Term and the Common Difference for the Arithmetic