Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = \left( \frac { 2 } { 5 } \right) ^ { n }$$
A) $\frac { 2 } { 5 } , \frac { 4 } { 25 } , \frac { 8 } { 125 } , \frac { 16 } { 625 }$
B) $1 , \frac { 2 } { 5 } , \frac { 4 } { 25 } , \frac { 8 } { 125 }$
C) $\frac { 2 } { 5 } , \frac { 2 } { 10 } , \frac { 2 } { 15 } , \frac { 2 } { 20 }$
D) $1 , \frac { 4 } { 25 } , \frac { 8 } { 125 } , \frac { 16 } { 625 }$

Question

Quizplus · Accepted Answer

We can find the first four terms of the sequence by substituting n = 1, 2, 3, and 4 in the given expression for the general term. This gives us:
$$a_1 = \left(\frac{2}{5}\right)^1 = \frac{2}{5}$$
$$a_2 = \left(\frac{2}{5}\right)^2 = \frac{4}{25}$$
$$a_3 = \left(\frac{2}{5}\right)^3 = \frac{8}{125}$$
$$a_4 = \left(\frac{2}{5}\right)^4 = \frac{16}{625}$$
Therefore, the first four terms of the sequence are $\frac{2}{5}, \frac{4}{25}, \frac{8}{125}, \frac{16}{625}$, which correspond to choice A.

Write the First Four Terms of the Sequence Whose General an=(25)na _ { n } = \left( \frac { 2 } { 5 } \right) ^ { n }an​=(52​)n

Write the First Four Terms of the Sequence Whose General $a _ { n } = \left( \frac { 2 } { 5 } \right) ^ { n }$