- Which choice shows the product of 22 and 49?
- Which of the following is not a series?
a) Arithmetic series
b) Geometric series
c) Isometric series
d) Harmonic series
- Find sum of series 2+3+5+7?
a) 5
b) 10
c) 17
d) infinit
The correct answer and explanation is:
- The product of 22 and 49 is: 22×49=107822 \times 49 = 1078
- The correct answer is:
c) Isometric series
An arithmetic series has a constant difference between terms, a geometric series has a constant ratio, and a harmonic series consists of reciprocals of an arithmetic sequence. There is no such thing as an isometric series in mathematics. - Sum of the series 2 + 3 + 5 + 7:
The correct answer is c) 17 because: 2+3+5+7=172 + 3 + 5 + 7 = 17
Explanation (300 words):
A series in mathematics refers to the sum of terms in a sequence. In this problem, the sequence consists of prime numbers: 2, 3, 5, and 7. Prime numbers are natural numbers greater than 1 that have only two factors: 1 and themselves.
The given series: 2+3+5+72 + 3 + 5 + 7
is a finite arithmetic sum of the first four prime numbers. Since there are only four terms, the summation is straightforward: 2+3=52 + 3 = 5 5+5=105 + 5 = 10 10+7=1710 + 7 = 17
Thus, the correct answer is 17.
Understanding Different Types of Series:
- Arithmetic Series: Each term increases by a constant difference. Example: 2, 4, 6, 8, …
- Geometric Series: Each term is multiplied by a constant ratio. Example: 2, 4, 8, 16, …
- Harmonic Series: Sum of reciprocals of an arithmetic sequence. Example: 1 + 1/2 + 1/3 + 1/4 + …
- Prime Number Series: A sequence consisting only of prime numbers.
Since the given series consists of prime numbers, it does not follow an arithmetic or geometric rule but remains a simple summation of finite terms.
Now, I’ll generate an image related to this.
Here is the image representing the sum of the prime number series 2+3+5+7=172 + 3 + 5 + 7 = 17 on a chalkboard. Let me know if you need any modifications!
