- Express \(49\) as the sum of \(7 \) odd numbers.
- Express \(121\) as the sum of \(11\) odd numbers.
- Express \(49\) as the sum of \(7 \) odd numbers.
- Express \(121\) as the sum of \(11\) odd numbers.
Solution and Explanation
We know that the sum of first \(n\) odd natural numbers is \(n^2\).
(i) \(49 = (7)^2\)
Therefore, \(49\) is the sum of first \(7\) odd natural numbers.
\(49 = 1 + 3 + 5 + 7 + 9 + 11 + 13\)
(ii) \(121 = (11)^2\)
Therefore, \(121\) is the sum of first \(11\) odd natural numbers.
\(121 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21\)
Top Questions on Some More Interesting Patterns
- The following numbers are obviously not perfect squares. Give reason.
- 1057
- 23453
- 7928
- 222222
- 64000
- 89722
- 222000
- 505050
- CBSE Class VIII
- Mathematics
- Some More Interesting Patterns
- Without adding find the sum
- \(1 + 3 + 5 + 7 + 9\)
- \(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 \)
- \(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23\)
- CBSE Class VIII
- Mathematics
- Some More Interesting Patterns
- How many numbers lie between squares of the following numbers?
- \(12\) and \(13\)
- \(25\) and \(26\)
- \(99\) and \(100\)
- CBSE Class VIII
- Mathematics
- Some More Interesting Patterns
- Using the given pattern, find the missing numbers.
\(1^ 2 + 2^2 + 2^2 = 3^2\)
\(2^ 2 + 3^2 + 6^2 = 7^2 \)
\(3^ 2 + 4^2 + 12^2 = 13^2 \)
\(4 ^2 + 5^2 + ....^2 = 21^2 \)
\(5^ 2 +....^2 + 30^2 = 31^2\)
\(6^ 2 + 7^2 + ....^2 = ....^2\)- CBSE Class VIII
- Mathematics
- Some More Interesting Patterns
- Observe the following pattern and supply the missing number.
\(11^2 = 121\)
\(101^2 = 10201\)
\(10101^2 = 102030201\)
\(1010101^2 = …\)
\(...^2= 10203040504030201\)- CBSE Class VIII
- Mathematics
- Some More Interesting Patterns
Questions Asked in CBSE Class VIII exam
- Subtract 4p2q – 3pq + 5pq2 – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq2 + 5p2q
- CBSE Class VIII
- Addition and Subtraction of Algebraic Expressions
- Differentiate between regular and diffused reflection. Does diffused reflection mean the failure of the laws of reflection?
- CBSE Class VIII
- Regular and Diffused Reflection
Fill in the blanks in the sentences below (the verbs given in brackets will give you a clue).
(i) The earth trembled, but not many people felt the ____. (tremble)
(ii) When the zoo was flooded, there was a lot of _____ and many animals escaped into the countryside. (confuse)
(iii) We heard with _____ that the lion had been recaptured. (relieve)
(iv) The zookeeper was stuck in a tree and his _____ was filmed by the TV crew. (rescue)
(v) There was much _____ in the village when the snake charmer came visiting. (excite)
- CBSE Class VIII
- The Tsunami
- Fill in the blanks with suitable words.
- Time taken by an object to complete one oscillation is called ___ .
- Loudness is determined by the ___ of vibration.
- The unit of frequency is ___.
- Unwanted sound is called __________ .
- Shrillness of a sound is determined by the ___ of vibration.
- CBSE Class VIII
- Sound Produced by Humans
- Add the following. l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl
- CBSE Class VIII
- Addition and Subtraction of Algebraic Expressions