Question

The sum of 5 consecutive odd integer is 685. What are the numbers

Answer 1

Answer:

Numbers, required here, are 133 , 135 , 137 , 139 and 141.

Step-by-step explanation:

Let the required consecutive odd integers are 2a - 5 , 2a - 3 , 2a - 1 , 2a + 1 , 2a + 3

According to the question : -

⇒ Sum of 5 consecutive odd integers = 685

= > ( 2a - 5 ) + ( 2a - 3 ) + ( 2a - 1 ) + ( 2a + 1 ) + ( 2a + 3 ) = 685

= >  2a - 5 + 2a - 3 + 2a - 1 + 2a + 1 + 2a + 3 = 685

= >  2a + 2a + 2a + 2a + 2a - 5 - 1 + 1 - 3 + 3 = 685

= >  10a - 5 = 685

= >  10a = 685 + 5

= >  10a = 690

= >  a = 690 / 10

= >  a = 69

Therefore, required consecutive odd numbers are : -

2a - 5 = 2( 69 ) - 5 = 138 - 5 = 133

2a - 3 = 138 - 3 = 135

2a - 1 = 138 - 1 = 137

2a + 1 = 138 + 1 = 139

2a + 3 = 138 + 3 = 141

Required numbers are 133 , 135 , 137 , 139 , 141.

Answer 2

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Let first odd integer be x

•°• Second consecutive odd integer be x+2

•°•Third consecutive odd integer be x+4

•°•Fourth consecutive odd integer be x+6

•°• and Fifth consecutive odd integer be x+8

Given that,

=> sum of the five consecutive odd integer =685

=>x+x+2+x+4+x+6+x+8=685

=>5x+ 20=685

=>5x. = 685-20

=>5x. = 665

=>x. = 133

So, we get the first odd integer => x = 133

Now,

Second consecutive odd integer = x+2=133+2=135

•°•Third consecutive odd integer = x+4=133+4=137

•°•Fourth consecutive odd integer =x+6=133+6=139

•°• and Fifth consecutive odd integer = x+8=133+141

Hence,

$\sf{The \:five \:consecutive\: odd \:integers\\ \\ whose\: sum.\: is \:685\: are\: 133,135,137,139,141}$

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