Question

Winnie adds the smallest 30 positive even numbers. Grogg adds the largest 30 odd negative numbers. How much greater is Winnie's sum than Grogg's sum?

Answer 1

Answer:

1830

Step-by-step explanation:

Sum of smallest 30 positive even numbers is given by

2 + 4 + 6 + 8 + ......... up to 30 terms

= 2 ( 1 + 2 + 3 + 4 + ....... + 30)

= $2 \times \frac{1}{2} \times (30) \times (30+1) = 930$

Again the sum of largest 30 odd negative numbers is given by

- 1 - 3 - 5 - 7 - ...... up to 30 terms.

= - (1 + 3 + 5 + 7 + ...... up to 30 terms)

{This is an A.P. series having first term 1, common difference 2 and the number of terms 30}

= $-\frac{30}{2} [2 \times 1 + (30-1) \times 2]$

= - 900

Now, Winnie has the sum 930 and Grogg has the sum - 900.

So, Winnie's sum is (930 + 900) = 1830 more than Grogg's sum. (Answer)