Find the indicated term of the sequence.
-The twenty-fifth term of the arithmetic sequence $6 \sqrt { 3 } , 2 \sqrt { 3 } , - 2 \sqrt { 3 } , \ldots$
A) $106 \sqrt { 3 }$
B) $- 90 \sqrt { 3 }$
C) $102 \sqrt { 3 }$
D) $- 94 \sqrt { 3 }$

Question

Quizplus · Accepted Answer

The common difference $d$ of the sequence is $2\sqrt{3} - 6\sqrt{3} = -4\sqrt{3}$. The $n$th term of an arithmetic sequence is given by $a_n = a_1 + (n-1)d$. Substituting $a_1 = 6\sqrt{3}$, $d = -4\sqrt{3}$, and $n = 25$, we get $a_{25} = 6\sqrt{3} + (25-1)(-4\sqrt{3}) = 6\sqrt{3} - 96\sqrt{3} = -90\sqrt{3}$.

Find the Indicated Term of the Sequence 63,23,−23,…6 \sqrt { 3 } , 2 \sqrt { 3 } , - 2 \sqrt { 3 } , \ldots63​,23​,−23​,…

Find the Indicated Term of the Sequence $6 \sqrt { 3 } , 2 \sqrt { 3 } , - 2 \sqrt { 3 } , \ldots$