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

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) $- \frac { 3 } { 5 }$

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 common difference $d$ can be calculated using the formula $d = \frac{a_n - a_m}{n - m}$, where $n$ and $m$ are the positions of the two known terms. Substituting the given values, we get $d = \frac{-\frac{147}{5} - (-\frac{51}{5})}{45 - 13} = \frac{-\frac{96}{5}}{32} = -\frac{3}{5}$. Knowing the common difference, we can find $a_3$ by working backwards from one of the given terms, for example, $a_{13} = -\frac{51}{5}$. Since $a_{13}$ is 10 positions ahead of $a_3$, we add the common difference 10 times to $a_{13}$ to find $a_3$: $a_3 = a_{13} + 10d = -\frac{51}{5} + 10(-\frac{3}{5}) = -\frac{51}{5} - \frac{30}{5} = -\frac{81}{5} = -\frac{21}{5}$.

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 $\mathrm { a } _ { 45 } = - \frac { 147 } { 5 } , \mathrm { a } _ { 13 } = - \frac { 51 } { 5 } ; \mathrm { a } _ { 3 }$