Find the indicated term using the given information.
-$$\mathrm { a } _ { 45 } = - \frac { 147 } { 5 } , \mathrm { a } _ { 13 } = - \frac { 51 } { 5 } ; \mathrm { a } _ { 3 }$$
A) $- \frac { 21 } { 5 }$
B) 15
C) $- \frac { 24 } { 5 }$
D) $- \frac { 3 } { 5 }$

Question

Quizplus · Accepted Answer

Given two terms of an arithmetic sequence, $a_{45} = -\frac{147}{5}$ and $a_{13} = -\frac{51}{5}$, we can find the common difference and then use it to find $a_3$. The difference in term numbers is $45 - 13 = 32$, and the difference in term values is $-\frac{147}{5} - (-\frac{51}{5}) = -\frac{96}{5}$. The common difference $d = \frac{-\frac{96}{5}}{32} = -\frac{3}{5}$. Starting from $a_{13} = -\frac{51}{5}$, to find $a_3$, we move 10 terms back (since $13 - 3 = 10$), which is $10 \times -\frac{3}{5} = -\frac{30}{5} = -6$. Adding this to $a_{13}$ gives $a_3 = -\frac{51}{5} - 6 = -\frac{51 + 30}{5} = -\frac{81}{5} = -\frac{21}{5}$.

Find the Indicated Term Using the Given Information a45=−1475,a13=−515;a3\mathrm { a } _ { 45 } = - \frac { 147 } { 5 } , \mathrm { a } _ { 13 } = - \frac { 51 } { 5 } ; \mathrm { a } _ { 3 }a45​=−5147​,a13​=−551​;a3​

Find the Indicated Term Using the Given Information $\mathrm { a } _ { 45 } = - \frac { 147 } { 5 } , \mathrm { a } _ { 13 } = - \frac { 51 } { 5 } ; \mathrm { a } _ { 3 }$