From the given terms of the arithmetic sequence, find a1 and d.
-$a _ { 12 } = 50$ and $a _ { 25 } = 89$
A) $a _ { 1 } = 17 , d = 3$
B) $a _ { 1 } = 20 , d = 3$
C) $a _ { 1 } = 2 , d = 4$
D) $a _ { 1 } = 14 , d = 3$

Question

Quizplus · Accepted Answer

The formula for the nth term of an arithmetic sequence is $a_n = a_1 + (n - 1)d$. Given $a_{12} = 50$ and $a_{25} = 89$, we can set up two equations:1. $50 = a_1 + 11d$2. $89 = a_1 + 24d$Subtracting the first equation from the second gives $39 = 13d$, so $d = 3$. Substituting $d = 3$ into the first equation gives $50 = a_1 + 33$, so $a_1 = 17$.

From the Given Terms of the Arithmetic Sequence, Find A1 a12=50a _ { 12 } = 50a12​=50

From the Given Terms of the Arithmetic Sequence, Find A1 $a _ { 12 } = 50$