Question

find the first five term of geometric progression if a is equal to 1024 and R is equal to 1 by 2 ​

Answer 1

The first five term of G.P are 1024,512,256,128,64.

Step-by-step explanation:

Given : Geometric progression with a=1024 and $r=\frac{1}{2}$.

To find : The first five term of G.P. ?

Solution :

The geometric series is in form $a,ar,ar^2,ar^3,ar^4$

First term is a=1024

Second term is $ar=(1024)(\frac{1}{2})=512$

Third term is $ar^2=(1024)(\frac{1}{2})^2=1024\times \frac{1}{4}=256$

Fourth term is $ar^3=(1024)(\frac{1}{2})^3=1024\times \frac{1}{8}=128$

Fifth term is $ar^4=(1024)(\frac{1}{2})^4=1024\times \frac{1}{16}=64$

Therefore, the first five term of G.P are 1024,512,256,128,64.

#Learn more

The sixth term of a geometric sequence is 23 and the tenth term is 5103. find the geometric sequence.

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Answer 2

The first five terms of geometric progression(GP) are 1024, 512, 256, 128 and 64.

Step-by-step explanation:

Given,

First term (a) = 1024 and common ratio (r) = $\dfrac{1}{2}$

To find, the first five term of G.P. = ?

The first five term of geometric progression are:

a, $ar,ar^{2} ,ar^{3},ar^{r}$

∴ First term = a = 1024,

Second term = ar = $1024\times \dfrac{1}{2}$ = 512

Third term = a$r^2$ = $1024\times \dfrac{1}{2^2}$ = 256

Fourth term = a$r^3$ = $1024\times \dfrac{1}{2^3}$ = 128

Fifth term = a$r^4$ = $1024\times \dfrac{1}{2^4}$ = 16

Thus, the first five terms of G.P are 1024, 512, 256, 128 and 64.