Geometric Progression I

2 power 1 is 2 , 2 power 2 is 4 and so on ...we reach 2 power 20 which is 20th term and answer is 1048576

Use your calculator to count 2^20 :p

as for geometric progression,

a = 2 , r = 4/2 = 8/4 = 16/8 = 2,

by applying Tn = ar^(n-1) ,

T20 = 2 . 2^(19) = 1 048 576,

thanks...

The formula for a geometric progression to identify the nth term can be found by the following formula: $\large ar^{n - 1}$ where $a$ is the first term and $r$ is the common ratio of the sequence. By substituting we get:

$\large \color{#3D99F6} 2\times 2^{20 - 1} = \color{#20A900} 2^{20} = \color{magenta} \boxed{1048576 }$

The pattern of the last digit is 2,4,8,6 and it is repeating (2^1,2^2,2^3,2^4,.... )

We need to find the 20th term (2^20). It will definitely end with 6.

The only given answer end with 6 is 1048576.

Hence the solution is 1048576.

Nth term of a G.P = ar^{N -1} where a is the first term & r is the common ratio => 20th term of this G.P = 2 * 2^19 = 1048576

This solutions is when no options are available

as for geometric progression,
a = 2 , r = 4/2 = 8/4 = 16/8 = 2,
by applying Tn = ar^(n-1) ,
T20 = 2 . 2^(19) = 2^10 * 2^10 = 1024 * 1024 =

now,

to multiply 1024 * 1024
1. keep 10 to the right 
2. get product of the last 2 digits : 576
3. sum of the last 2 digits :  48


lets arrange to get the ans:
10 (sum of the last 2 digits) (product of the last 2 digits)
So, 10 48 576

$ar^{n-1}$

$2 \times 2^{20-1}$

$2 \times 2^{19}$

$\boxed{1048576}$

The only perfect power of $2$ listed is $1048576$

In the above sequence the formula is 2^position.

= 2 ^ 20

= 1048576

a=2; common ratio, r=2; n=20. Thus, 20th term = a(r^(n-1)) = 2*2^19 = 2^20 = 1048576

nth term = first term * common ratio raised to ( n - 1 )