Tag: some special sequences

Questions Related to some special sequences

If the square of a number ends with $10$ zeroes, how many zeroes will the number have at the end?

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. $5$

  2. $15$

  3. $30$

  4. $40$

Show answer
Correct Option: A
Explanation:

If the square of a number has $ 10 $ zeroes, the number will have $ 10 \div 2 = 5 $ zeroes.

If a number ends with 3 zeroes, how many zeroes will its square have at the end ?

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. 3

  2. 4

  3. 6

  4. 1

Show answer
Correct Option: C
Explanation:

If a number ends with $ 3 $ zeroes, then its square will have $ 3 \times 2 = 6 $ zeroes.

Express $49$ as the sum of $7$ odd numbers.
Express $121$ as the sum of $11$ odd numbers.

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. $1+3+5+7+9+11$
    $1+3+5+7+9+11+13+15+19$

  2. $1+3+5+7+9+11+13$
    $1+3+5+7+9+11+13+15+19+21$

  3. $1+3+5+7+9+11$
    $1+3+5+7+9+11+13+15+19+21$

  4. $1+3+5+7+9+11+13$
    $1+3+5+7+9+11+13+15+19$

Show answer
Correct Option: B
Explanation:

$49=7^2=$ sum of first $7$ odd numbers.
So, $49=1+3+5+7+9+11+13$.
Similarly, $121=11^2=$ sum of first $11$ odd numbers. 
So, $121=1+3+5+7+9+11+13+15+19+21$

Observe the following pattern and fill in the missing number. 
$ \displaystyle 11^{2} =121$
$ \displaystyle 101^{2} =10201$
$ \displaystyle 10101^{2} =102030201$
$ \displaystyle 1010101^{2} =......................$

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. $ \displaystyle 1010101^{2} $=10203030201

  2. $ \displaystyle 1010101^{2} $=10204040201

  3. $ \displaystyle 1010101^{2} $=1020304030201

  4. $ \displaystyle 1010101^{2} $=10204030201

Show answer
Correct Option: C
Explanation:

$11^{2}$$=$$121$

$101^{2}$$=$$10201$
$10101^{2}$$=$$10203020101$
$1010101^{2}$$=$$1020304030201$
$101010101^{2}$$=$$10203040504030201$
We will go up to number of  ones in the number numerically.
Hence, Option C is correct.

State whether true or false:

121 can be expressed as the sum of 11 odd numbers.

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

$\sum _1^n(2n+1)=n^2$

Sum of  n odd consecutive number$=n^2$
$1+3+5+7+9+11+13+15+17+19+21=(11)^2=121$  (as there are 11  odd numbers n=11)

Find the sum of the following odd numbers given .

$1+3+5+7+9+11+13$

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. $25$

  2. $36$

  3. $49$

  4. $100$

Show answer
Correct Option: C
Explanation:

Sum of odd numbers is $n^2$ where n is no. of odd nos.
n= 7 odd nos. 
Therefore sum is $7^2  = 49$

Find the value of the following without actually multiplying:

 $13 \times 15$

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. 165

  2. 145

  3. 156

  4. 195

Show answer
Correct Option: D
Explanation:

$13\times15$ $=$ $(10+3)$ $(10+5)$

$100+50+30+15$ $=$ $195$
Hence, Option D is correct.

Find the sum of the following series without actually adding it.

$1+3+5+7+9+11+13+15+17+19+21$

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. $101$

  2. $161$

  3. $121$

  4. $141$

Show answer
Correct Option: C
Explanation:

Given series is $1+3+5+7+9+11+13+15+17+21$

Sum of odd natural numbers is $=n^2$

where $n= $ number of odd numbers are $11$

So, sum of the series given is $=11^2= 121 $.

State whether true or false:

When an even number is given, square of this number will be even.

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

$28 \times  28 = 78\underline{4} $
$162 \times  162 = 262\underline{44}$
(last digit is 4 even , so whole number is even.)

Therefore, A is the correct answer.

Find the value of $7 \times 9$.

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. 64

  2. 63

  3. 53

  4. None of these

Show answer
Correct Option: B
Explanation:

$7\times9$ $=$ $(10-3)$ $(10-1)$

$100-30-10+3$ $=$ $63$
Hence, Option B is correct.