SOLUTION: When the sun if the first 31 positive even integers is added to the first 32 positive off integers the result is N find N

Question 1035847: When the sun if the first 31 positive even integers is added to the first 32 positive off integers the result is N find N
Answer by ikleyn(52908) (Show Source): You can put this solution on YOUR website!
.
When the sun if the first 31 positive even integers is added to the first 32 positive odd integers the result is N. Find N.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The sum of the first 31 positive even integers is the sum 

2 + 4 + 6 + . . . + 62.    (1)


The sum of the first 32 positive odd integers is the sum 

1 + 3 + 5 + . . . + 63.    (2)


When these two sums, (1) and (2) are added, the sum is

1 + 2 + 3 + 4 + 5 + 6 + . . . + 63.   (3)

 
It is the sum of the first 63 positive integers.


It is equal to  = 63*32 = 2016.


You can use the formula for the sum of an arithmetic progression (see the lesson Arithmetic progressions in this site) 

or use the fact that the sum of the first "n" positive integer numbers is    


See the same lesson or/and the following two lessons

    - The proofs of the formulas for arithmetic progressions 

    - Problems on arithmetic progressions 

in this site.

RELATED QUESTIONS
Find the sum of: a) the first odd 'n' odd positive integers b) the first 'n' even... (answered by Edwin McCravy)

if the third of the three consecutive positive odd integers is added to product of the... (answered by gc2000)

when the first of two consecutive positive integers is added to the square of the second (answered by Maths68)

The sum S of the first n consecutive even positive integers 2,4,6,...,2n is given by the... (answered by solver91311)

if the square of a positive integer is added to 6 times an integers, the result is 135.... (answered by mananth)

three consecutive even integers are such that if the second is added to twice the first... (answered by josmiceli)

Find the sum of the first 100 even positive... (answered by rfadrogane)

When the smaller of two consecutive even integers is added to three times the larger, the (answered by lauramg012)

Two positive integers. The sum of the integers is 27. When the first integer is added to... (answered by josgarithmetic,ikleyn)