Question

4 the second part please solve it

Answer 1

Answer:

1/4

5/8

25/16

125/32

625/64

Step-by-step explanation:

Given a Geometric Progression, GP.

The nth term of GP is given as,

$\dfrac{ {5}^{n - 1} }{ {2}^{n + 1} }$

We have to write the first five terms.

Here, n is the natural number.

So, we have to find the terms from n = 1 to 5.

n = 1

$= > t1 = \frac{ {5}^{1 - 1} }{ {2}^{1 + 1} } \\ \\ = > t1 = \frac{ {5}^{0} }{ {2}^{2} } \\ \\ = > t1 = \frac{1}{4}$

n = 2

$= > t2 = \frac{ {5}^{2 - 1} }{ {2}^{2 + 1} } \\ \\ = > t2 = \frac{5}{8}$

n = 3

$= > t3 = \frac{ {5}^{3 - 1} }{ {2}^{3 + 1} } \\ \\ = > t3 = \frac{25}{16}$

n = 4

$= > t4 = \frac{ {5}^{4 - 1} }{ {2}^{4 + 1} } \\ \\ = > t4 = \frac{125}{32}$

n = 5

$= > t5 = \frac{ {5}^{5 - 1} }{ {2}^{5 + 1} } \\ \\ = > t5 = \frac{625}{64}$

Hence, the first five terms of the given GP are, 1/4, 5/8, 25/16, 125/32 and 625/64.