Question

Which term of the geometric progression 1,2,4,8,....is 2048

Answer 1

Answer:

12 th term

Step-by-step explanation:

nth term in gp:

• nth term in gp
• $tn = a {r}^{n - 1}$
• n=unknown
• a = first term in gp which is 1
• r= ratio which is 2/1=4/2=8/4=2
• $2048 = 1 \times {2}^{n - 1}$

$n - 1 = log_{2}(2048)$

$n - 1 = 11$

$n = 12$

Answer 2

Answer:

2048 is 12th term of the given series

Step-by-step explanation:

Given geometric progression  1, 2, 4, ...2048

the general form of the geometric progression is  $a$, $ar$, $ar ^{2}$ .. $ar^{n-1}$

here common ratio r =  $\frac{ T_{ n}}{T_{n-1 } }$ , and nth term  $T_{n} = ar^{n-1}$  , a is the first term

the given series 1, 2, 3, 4, ..2048

first term a = 1

common ratio  $r = \frac{T_{2}}{T_{2-1} }$ =   $\frac{2}{1}$ = 2  

nth term = $ar ^{ n-1} =$  (1) $2^{ n-1}$

let 2048 be the nth term ⇒   $2^{n-1} =2048$

                                          ⇒  $2^{n} . 2^{-1} =2048$

                                          ⇒  $2^{n} . \frac{1}{2}$ = 2048

                                          ⇒  $2^{n} =2048 (2)$  [ $2^{11} =2048$]

                                          ⇒ $2^{12} = 4096$  

  ∴ 2048 is 12th term of the given series