Which term of the Geometric Progression 5,10,20,40...is 5120?

Question

First and last term of a geometric progression are 3 and 96. If the sum of all these terms is 189, then find the number of terms in this progression.

Answer 1

11th

5
10
20
40
80
160
320
640
1280
2560
5120

Answer 2

From geometric progression,

Gn =G_1 r^(n-1).............................1

but
Gn = 5120
G1 = 5
r = 10÷5
=2

5120 = 5 * 2^(n-1)

2^(n-1) = 5120\5
= 1024
= 2^(10)

i.e.
n - 1 = 10

so
n = 11

so it is 11th term.

Answer 3

Given the geometric progression:
a 1 = 5
a 2 = 5 x 2 = 10
a 3 = 10 x 2 = 20 or a 1 x 2^2 = 5 x 4 = 20
Then, we can write:
a n = a1 x 2 ^(n - 1) being n the term of the progression
Then,
an = 5120 = 5 x 2 ^(n-1)
Solving this equation
For n= 11 , 2 ^10 = 1024 , 1024 x 5 = 5120
The term is n= 11

Answer 4

Clearly:
The common ration = 10 / 5 = 2.
therefore, a = 5; r = 2;
As, we know,

a*r^n-1=5120
:5*2^n-1 = 5120
:2^n-1 = 1024
:2^n-1 = 2^ 10
: n - 1= 10
n = 11