Question

find the first five of gp if a=1024 and r=1/2​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The first five terms of GP is $a_1=1024,a_2=512,a_3=256,a_4=128,a_5=64$

Therefore the sequence is ${\{1024,512,256,128,64,...}\}$

Step-by-step explanation:

Given that the first term of GP  a=1024 and common ratio $r=\frac{1}{2}$

To find the first five terms of GP :

Since given sequence is geometric sequence  we can write the sequence

${\{a,ar,ar^2,....}\}$

The nth term of GP is $a_n=ar^{n-1}$

From the given $a_1=1024$

To find $a_2,a_3,a_4,a_5$

Put n=2 , a=1024 and  $r=\frac{1}{2}$ in $a_n=ar^{n-1}$ we get

$a_2=(1024)(\frac{1}{2})^{2-1}$

$=1024(\frac{1}{2})^1$

$=\frac{1024}{2}$

$=512$

Therefore $a_2=512$

Put n=3 , a=1024 and  $r=\frac{1}{2}$ in $a_n=ar^{n-1}$ we get

$a_3=(1024)(\frac{1}{2})^{3-1}$

$=1024(\frac{1}{2})^2$

$=1024(\frac{1}{4})$

$=\frac{1024}{4}$

$=256$

Therefore $a_3=256$

Put n=4 , a=1024 and  $r=\frac{1}{2}$ in $a_n=ar^{n-1}$ we get

$a_4=(1024)(\frac{1}{2})^{4-1}$

$=1024(\frac{1}{2})^3$

$=1024(\frac{1}{8})$

$=\frac{1024}{8}$

$=128$

Therefore $a_4=128$

Put n=5 , a=1024 and  $r=\frac{1}{2}$ in $a_n=ar^{n-1}$ we get

$a_5=(1024)(\frac{1}{2})^{5-1}$

$=1024(\frac{1}{2})^4$

$=1024(\frac{1}{16})$

$=\frac{1024}{16}$

$=64$

Therefore $a_5=64$

Therefore the sequence is ${\{1024,512,256,128,64,...}\}$

The first five terms of GP is $a_1=1024,a_2=512,a_3=256,a_4=128,a_5=64$