)Find the sum of the first 50 even numbers . Thank you.

Question

First 50 even numbers.

Answer 1

Anna,

 

Use the same trick I showed you on your previous problem.

First divide the sequence by 2 to convert it to a new sequence:  1 2 3 ... 50  where n = 50 entries.

Sum of new sequence = n(n + 1)/2 = 50(51)/2 =1275

Now multiply that by your earlier divisor of 2 to get back to your real sequence = 2(1275) = 2,550.

 

BTW, another interpretation.  What's the average number in the 1 2 3 ... 50 sequence?  Why it's just the first added to the last and divided by 2 = (1 + n)/2.  Now just multiply this average by the number of consecutive entries, n, so the sum becomes n times (n + 1)/2, where n can be any finite sequence ender for the integers.