Question

Let a sequence have 1,000 zeroes. In step 1 we add 2 to every position. In step 2 we add 2 to every even position. In step 3 every position that is a multiple of 3, we add 2. This is continued up to the thousandth step. After 1,000th step what is the value of the 600th position?

Answer 1

Answer:

48

Step-by-step explanation:

Let the sequence be a₁,a₂,a₃,a₄,a₅,.........a₁₀₀₀.

Step 1: Every position in the sequence is increased by 2.

Step 2: Every even position in the sequence is increased by 2.

Step 3: Every  3rd term in the sequence is increased by 2.

........

Analysis:

a₁ is added by 2 only in step 1

a₂ is added by 2 in  steps 1 and 2

a₃ is added by 2 in steps 1 and 3

............

Clearly it is evident that any term aₓ is added by 2 in step n ,

if and only if n is the factor of x.

Now, if we factorize 600 we get , 600 =2³×3×5².

Thus total number of factors of 600 are (1+3)×(1+1)×(1+2) = 24.

So,  during each of these 24 steps a₆₀₀ will be added by 2.

Thus a₆₀₀ would be added by 2  24 times , hence a₆₀₀ would be

increased by 24×2 = 48.