Question

What is the value of

Answer 1

Answer:

9900

Step-by-step explanation:

Take each group of 4 consecutive integers and find their sum. Since there is a total of 200 numbers, there are 50 groups of 4 numbers.

1 + 2 + 3 - 4 = 2

5 + 6 + 7 - 8 = 10

9 + 10 + 11 - 12 = 18

13 + 14 + 15 - 16 = 26

...

197 + 198 + 199 - 200 = 394

We see a pattern.

2 + 10 + +18 + 26 + ...  + 394

a_1 = 2; a_50 = 394; d = 8

Now we sum the terms of this series of 50 terms.

S_n = (n/2)(a_1 + a_n)

S_50 = (50/2)(2 + 394)

S_50 = 9900