Answer:
The correct option is D. The sum first 10 even numbers is 10x11.
Step-by-step explanation:
The first even number is 2 and the sum of first even term is 2. The product form of the sum is
\(1\times 2\)
The first two even number are 2,4 and the sum of first two even terms is 6. The product form of the sum is
\(2\times 3\)
The first three even number are 2,4,6 and the sum of first three even terms is 12. The product form of the sum is
\(3\times 4\)
The product form of the sum of ever term follows pattern. It is the product of n and (n+1), where n is the first n even numbers.
\(n\times (n+1)\)
The pattern can be derived.
The sum of first n even numbers is
\(S_n=2+4+6+8+---+2n\)
\(S_n=2(1+2+3+4+---+n)\)
\(S_n=2(\frac{n}{2})(2(1)+(n-1)1)\)
\(S_n=n(2+n-1)\)
\(S_n=n(n+1)\)
Therefore the sum of first 10 even numbers is
\(S_{10}=10\times (10+1)\)
\(S_{10}=10\times (11)\)
Therefore option D is correct.
