Solve the problem.
-Find the nth term of the following arithmetic sequence: $2,2 + \sqrt { 5 } , 2 + 2 \sqrt { 5 } , \ldots$
A) $2 + 5 ( \mathrm { n } - 1 )$
B) $2 + 5 n$
C) $2 + n \sqrt { 5 }$
D) $2 + ( n - 1 ) \sqrt { 5 }$

Question

Quizplus · Accepted Answer

The common difference of the sequence is $\sqrt{5}$, so the nth term is given by the formula for the nth term of an arithmetic sequence: $a_n = a_1 + (n - 1)d$, where $a_1 = 2$ and $d = \sqrt{5}$. Substituting these values gives $a_n = 2 + (n - 1)\sqrt{5}$.

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Solve the Problem $2,2 + \sqrt { 5 } , 2 + 2 \sqrt { 5 } , \ldots$