Question

find the first five termsofgeometrical progression if a=1024 and r=1/2​

Answer 1

Answer:

ok so basically formula is a for second term it is ar

for third term it is

${ar}^{2}$

for fourth term it is

$ar ^{3}$

for fifth term it is

$ar ^{5}$

so first term is 1024

second term will be a ×r that is 1024(1/2) = 1024/2 = 512

third term a × r square = 1024(1/2)^2 = 1024(1/4) = 1024/4 = 256

fourth term a×r ^3 = 1024(1/2)^3 = 1024(1/8) = 1024/8 = 125

and last fifth term a×r^4 = 1024(1/2)^4 = 1024(1/16) = 1024/16 = 64

so first 5 terms are :

1024,512,256,125,64

DONE......

Answer 2

The first five terms of Geometric sequence is

$a_1=1024$,$a_2=512$,$a_3=256$,$a_4=128$ and $a_5=64$

Step-by-step explanation:

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

To find the first five terms for the given Geometric sequence :

• We know the nth term of the Geometric sequence is $a_n=ar^{n-1}$
• The geometric sequence is ${\{a,ar,ar^2,ar^3,...}\}$
• Now to find the first five terms of GP so that we have

${\{a,ar,ar^2,ar^3,ar^4}\}$

• Put n=1 and $r=\frac{1}{2}$ in $a_n=ar^{n-1}$

$a_1=(1024)(\frac{1}{2})^{1-1}$

$=(1024)(\frac{1}{2})^{0}$

$=1024(1)$

Therefore $a_1=1024$

• Put n=2 and $r=\frac{1}{2}$ in $a_n=ar^{n-1}$

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

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

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

Therefore $a_2=512$

• Put n=3 and $r=\frac{1}{2}$ in $a_n=ar^{n-1}$

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

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

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

Therefore $a_3=256$

• Put n=4 and $r=\frac{1}{2}$ in $a_n=ar^{n-1}$

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

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

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

Therefore $a_4=128$

• Put n=5 and $r=\frac{1}{2}$ in $a_n=ar^{n-1}$

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

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

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

Therefore $a_5=64$

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

The first five terms of Geometric sequence is

$a_1=1024$,$a_2=512$,$a_3=256$,$a_4=128$ and $a_5=64$