5)Mr. Bean chooses a number and he keeps on doubling the number followed by subtracting one from it, if he chooses 3 as initial number and he repeats the operation for 30 times then what is the final result?
a. (2^30) – 1 b. (2^30) – 2
c. (2^31) – 1 d. 2^31 + 1
Answers
Answer:
2³¹ + 1
Step-by-step explanation:
Bean chooses a number and he keeps on doubling the number followed by subtracting one from it, if he chooses 3 as initial number and he repeats the operation for 30 times then what is the final result?
initial Number = 3
After 1 st operation = 3 *2 - 1 = 5
Afer 2nd operation = 5*2 - 1 = 9
After 3rd operation = 9*2 - 1 = 17
After 4th Operation = 17*2 - 1 = 33
After 5th operation = 33*2 - 1 = 65
3 5 9 , 17 , 33 , 65
2 4 8 16 32
NUmber after 1st operation = 3 + 2
Number after 2nd opeartion = 3 + 2 + 4
Number after 3rd opeartion = 3 + 2 + 4 + 8
and so on
Number after 30 operations
3 + ( 2 + 4 + 8 + ............................................+ 30th Term)
2 + 4 + 8 + ............................................+ 30th Term
a = 2
r = 2
Sum of 30 terms = 2 * (2³⁰ - 1)/(2-1) = 2³¹ - 2
3 + 2³¹ - 2
= 2³¹ + 1