What is the prime factorization of 12
2 answers:
Answer: 2 × 2 × 3
Step-by-step explanation: To start off this problem, notice that 12 can be factored into 2 × 6.
Since 2 is a prime number, we move onto the 6. The number 6 is not a prime number and it can be factored into 2 × 3.
Since 2 and 3 are prime numbers, we are finished factoring.
If we bring down the 2 we had from the first factoring step, we can see that the prime factorization of 12 is 2 × 2 × 3.
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Given:
The different recursive formulae.
To find:
The explicit formulae for the given recursive formulae.
Solution:
The recursive formula of an arithmetic sequence is and the explicit formula is
, where a is the first term and d is the common difference.
The recursive formula of a geometric sequence is and the explicit formula is
, where a is the first term and r is the common ratio.
The first recursive formula is:
for
.
It is the recursive formula of an arithmetic sequence with first term 5 and common difference 5. So, the explicit formula for this recursive formula is:
Therefore, the correct option is A, i.e., .
The second recursive formula is:
for
.
It is the recursive formula of a geometric sequence with first term 5 and common ratio 3. So, the explicit formula for this recursive formula is:
Therefore, the correct option is F, i.e., .
The third recursive formula is:
for
.
It is the recursive formula of an arithmetic sequence with first term 5 and common difference 3. So, the explicit formula for this recursive formula is:
Therefore, the correct option is D, i.e., .
Answer:
Option (D)
Step-by-step explanation:
All rational and irrational numbers are real numbers.
{-2, -1, -1.8, 0, 1, 2.......}
Numbers written in the form of are rational numbers. They are the part of irrational numbers.
{-2.5, -2, -1, 0, 1, 2.....}
Whole numbers with negative or positive notation are integers.
{-3, -2, -1, 0, 1, 2, 3, 4......}
Positive integers are the whole numbers (including zero).
{0, 1, 2, 3, 4, .......}
All whole numbers excluding zero are the natural numbers.
{1, 2, 3, 4,........}
Irrational numbers are the part of real numbers written in the form of .
{}
Therefore, comes under Irrational numbers.
Option (D) is the answer.