Question

Calculate the missing terms of the geometric sequence 2048,?,?,?,8

Answer 1

Answer: 2048, 512, 128, 32, 8

Step-by-step explanation:

Recognize 2048 is 2^11, as all hackers know

1024 is 2^10 :-). Also 8 is 2^3.

So this problem is exactly similar to filling in the geometric sequence starting at 10^11 = 100,000,000,000, with three intermediate values ending with 10^3 = 1000.

(100,000,000,000) = 10^11

1,000,000,000 = 10^9

10,000,000 = 10^7

100,000, = 10^5

(1,000) = 10^3

Or, it is exactly similar to filling in the arithmetic series 11, a, b, c, 3. That one is (11), 9, 7, 5, (3), where we subtract 2 each time.

$A_0 = 11$

$A_{n+1} = A_{n} - 2$

The answer is (2048), 512, 128, 32, (8) where we divide by 2^2 each time. Or (2^11), 2^9, 2^7, 2^5, (2^3).

$G_0 = 2^{11}=512$

$G_{n+1} = G_{n} / 2^2$