Question

The sum of four consecutive odd integers is 28458968. What is the second number? Any help pliz how to work out ???

Answer 1

An odd number can be expressed as 2k+1 for some integer k.
So the sum of four consecutive odd numbers can be expressed as
\[((2k + 1) - 4) + ((2k + 1) - 2) + (2k+1) + ((2k + 1) + 2)\]\[= (2k-3) + (2k-1) + (2k +1) + (2k+3)\]
Try to use that expression to get the answer.

Answer 2

As fruitbasket said, any odd number can be expressed as 2k+1 for any integer k. So four consecutive odd numbers are 2k+1, 2k+3, 2k+5 and 2k+7 and their sum is 8k+16. Therefore, 8k+16=28458968 and k=3557369

Answer 3

thanks mate for the helpful answer

Answer 4

Just make sure that you substitute k into whatever expression you used for the 2nd odd number to get its value.

Answer 5

expression above can work for both even and odd consecutive integers??

Answer 6

2k is always an even integer (as long as k is an integer) due to the factor of 2. Odd numbers are just even numbers with 1 added to them, so:

CONSECUTIVE EVEN NUMBERS:
\[2k + (2k + 2) + (2k + 4) + ...\]CONSECUTIVE ODD NUMBERS:
\[(2k+1) + (2k+3) + (2k+5)+...\]

Answer 7

If the first odd integer is x, then the second (the one you want to find) is x+2, the third is x+4, then the fourth is x+6. Since the sum is 28458968, add them all together:

\[\large x + (x+2) + (x+4) + (x+6) = 28458968 \]

Answer 8

thanks very much for your help