The sum of two consecutive odd numbers is 128. Find the numbers.

2 n + 1 ; 2 n + 3 − 2 co n sec u t i v e o dd in t e g ers w h ere n i s na t u r a l n u mb er ( 2 n + 1 ) + ( 2 n + 3 ) = 128 2 n + 1 + 2 n + 3 = 128 ( 2 n + 2 n ) + ( 1 + 3 ) = 128 4 n + 4 = 128 ∣ s u b t r a c t 4 f ro m b o t h s i d es 4 n = 124 ∣ d i v i d e b o t h s i d es b y 44 = 62 A n s w er : 63 ; 65 ​
o t h er so l u t i o n : 128 : 2 = 64 an s w er : 64 + 1 = 65 ​ 64 − 1 = 63 ​

Answered by Anonymous | 2024-06-10

Call the first odd number x. That means the next odd number would be x+2. For example, if the first odd number is 9 then the next one would be 11, which is why it is plus 2. Okay?
So then, x+x+2=128 2x+2=128 2x=126 x=63 x+2=65 The two consecutive numbers are 63 and 65

Answered by Anonymous | 2024-06-10

The two consecutive odd numbers that sum to 128 are 63 and 65. We define the first number as n and find n = 63. Therefore, the next successive odd number is 65.
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Answered by Anonymous | 2024-10-10