Question

Express 7³ as sum of 7 consecutive odd numbers.

Answer 1

let the first odd integer be x.
therefore , x+x+2+x+4+x+6+x+8+x+10+x+12=7^3
x+x+2+x+4+x+6+x+8+x+10+x+12= 343
=> 7x + 42 = 343
7x=301
x=301/7
x=43
therefore , 43+45+47+49+51+53+55= 343
or, 43+45+47+49+51+53+55=7^3

Answer 2

The answer is 43 + 45 + 47 + 49 + 51 + 53 + 55 = 7³

Given:

 7³

To find:

Express 7³ as sum of 7 consecutive odd numbers

Solution:

As we know 7³ = 343

Let x be a odd number

Then next 6 odd number will be x+2, x+4, x+6, x+8, x+10, x+12  

Sum of 7 odd number will be

x + x+2 + x+4 + x+6 + x+8 + x+10 + x+12  

= 7x + 42

From given data sum of these odd numbers = 343

⇒ 7x + 42 =  343  

⇒ 7x = 301

⇒ x = 43

Therefore, the 7 odd numbers are  43, 45, 47, 49, 51, 53, 55

⇒ 43 + 45 + 47 + 49 + 51 + 53 + 55 = 343

⇒  43 + 45 + 47 + 49 + 51 + 53 + 55 = 7³

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