Home
Class 8
MATHS
Observe the following pattern 1+3=2^2 ...

Observe the following pattern `1+3=2^2`
`1+3+5=3^2`
`1+3+5+7=4^2`
and write the value of `1+3+5+7+9+` upto n terms.

Text Solution

AI Generated Solution

To solve the problem, we need to find the value of the sum of the first n odd natural numbers, which is represented as: \[ 1 + 3 + 5 + 7 + 9 + \ldots \text{ (up to n terms)} \] ### Step-by-Step Solution: 1. **Identify the Pattern**: - The given sums are: ...
Promotional Banner

Topper's Solved these Questions

  • RATIONAL NUMBERS

    RD SHARMA|Exercise All Questions|185 Videos
  • TIME AND WORK

    RD SHARMA|Exercise All Questions|46 Videos

Similar Questions

Explore conceptually related problems

Observe the following pattern :1^(3)=11^(3)+2^(3)=(1+2)^(2)1^(3)+2^(3)+3^(3)=(1+2+3)^(2) Write the next three rows and calculate the value of 1^(3)+2^(3)+3^(3)++9^(3)+10^(3) by the above pattern.

Find the sum of the series 1+3x+5x^(2)+7x^(3)+...... upto n terms.

If 1**2=1,2**3=-1 and 3**4=-5 , then find the value of 7**9=?

If [(1, 2),( 3, 4)][(3, 1),( 2, 5)]=[(7, 11),( 23, k)] , then write the value of kdot

What should come next in the following series? 1 2 3 4 5 6 7 8 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 7 6 5 4 3 2 1 1 2 3

Find the sum of the series 1*2*3+2*3*4+3*4*5+"...." " upto n terms " .

Find the sum of the following series to n term: 3.1^2+5.2^2+7.3^2+……..

The sum of the the series 1+2x3+3x5+4x7+.... Upto 11^(th) term is

If [[1,2],[3,4]] [[3,1],[2,5]]=[[7,11],[k,23]], then write the value of k.

What should come next in the following number series ? 9 7 5 3 1 1 8 6 4 2 2 9 7 5 3 1 1 8 6 4 2 2 9 7 5 3 1 1 8 6 4 2 2 9 7 5 1) 1 2) 5 3) 3 4) 5 5) None of these

RD SHARMA-SQUARES AND SQUARE ROOTS-All Questions
  1. The square of which of the following numbers would be an odd numbers...

    Text Solution

    |

  2. What will be the units digit of the squares of the following numbers...

    Text Solution

    |

  3. Observe the following pattern 1+3=2^2 1+3+5=3^2 1+3+5+7=4^2 and...

    Text Solution

    |

  4. Observe the following pattern 2^2-1^2=2+1 3^2-2^2=3+2 4^2-3^2=4+3 ...

    Text Solution

    |

  5. Which of the following triplets are Pythagorean? (I)(8,\ 15 , 17) ...

    Text Solution

    |

  6. Observe the following pattern (1xx2)+(2xx3)=(2xx3xx4)/3, (1xx2)+(2xx3...

    Text Solution

    |

  7. Observe the following pattern 1=1/2{1xx(1+1)}, 1+2=1/2{2xx(2+1)}, 1...

    Text Solution

    |

  8. Observe the following pattern (i)1^2=1/6[1xx(1+1)xx(2xx1+1)], (ii)1^...

    Text Solution

    |

  9. Which of the following square numbers are squares of even numbers ? ...

    Text Solution

    |

  10. By just examining the units digits, can you tell which of the follow...

    Text Solution

    |

  11. Write five numbers for which you cannot decide whether they are squa...

    Text Solution

    |

  12. Write five numbers which you connot decide whether they are square ...

    Text Solution

    |

  13. Find the square root of the following number by prime factorization....

    Text Solution

    |

  14. Find the squares of the following numbers using column method. (I)25...

    Text Solution

    |

  15. Find the squares of the following numbers using column method: (I)99...

    Text Solution

    |

  16. Find the squares of the following numbers by visual method. (I)54   ...

    Text Solution

    |

  17. Find the square of the following numbers by visual method: (I)205   ...

    Text Solution

    |

  18. Find the squares of the following using diagonal method: (I)89     ...

    Text Solution

    |

  19. Find the square of the following numbers by diagonal method: (I)349 ...

    Text Solution

    |

  20. Find the squares of the following numbers: (I)65            (ii)    ...

    Text Solution

    |