Question

Given a sequence of ten numbers, if the first number is 2 and each other number is the square of the preceding term then the 10th number is
A) between 10^10 and 10^15
B) between 10^25 and 10^50
C) between 10^50 and 10^75
D) more than 10^100
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Answer 1

Given :- a sequence of ten numbers, if the first number is 2 and each other number is the square of the preceding term then the 10th number is

A) between 10^10 and 10^15

B) between 10^25 and 10^50

C) between 10^50 and 10^75

D) more than 10^100 .

Solution :-

1. first number of sequence = 2
2. second number = (first number)² = (2)² = 4
3. Third number = (second number)² = (4)² = 16
4. Fourth number = (16)² = 256
5. 5th number = (256)²
6. 6th number = {(256)²}² = (256)⁴
7. 7th number = {(256)⁴}² = (256)⁸ { (x^a)^b= x^(a*b). }
8. 8th number = {(256)⁸}² = (256)¹⁶
9. 9th number = {(256)¹⁶}² = (256)³²
10. 10th number = {(256)³²}² = (256)⁶⁴

Now,

→ 10th number = (256)⁶⁴

→ 10th number = {(16)²}⁶⁴

→ 10th number = (16)^(2 * 64)

→ 10th number = (16)¹²⁸

Therefore,

• 10¹⁰⁰ < 16¹²⁸ .

Hence, the 10th number of the sequence is (D) more than 10^100 .

Learn more :-

. How many numbers up to 700 are divisible by 4 or 5?

https://brainly.in/question/26649471

Answer 2

Step-by-step explanation:

1. using 2=10/5 this problem can be done