Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.2 Arithmetic Sequences and Series - 14.2 Exercise Set - Page 902: 32

$a_1=2$ $d=2$

We have an arithmetic sequence in which $a_{12}=24$ and $a_{25}=50.$ In order to find $a_{1}$ and $d$ we will use the fact that any term of arithmetic sequence is expressed through the formula $a_{n}=a_1+d(n-1)$ Hence, $a_{12}=a_1+d\cdot11$ $a_{25}=a_1+d\cdot24$ $a_{25}-a_{12}=a_1+d\cdot24-a_1-d\cdot11=d(24-11)=13d$ $50-24=13d$ So $d=2$ Nowe we can use any equation to find $a_1.$ $24=a_1+2\cdot11$ $a_1=2$