Tag: some special sequences

Questions Related to some special sequences

Find the value of $11\times 13$.

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

  1. 143

  2. 163

  3. 173

  4. None of these

Show answer
Correct Option: A
Explanation:

$11\times13$ $=$ $(10+1)$ $(10+3)$

$100+30+1+3$ $=$ $143$
Hence, Option A is correct.

Find the sum of:
$1+3+5+7+9+11+13+15+17+19+21+23$

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

  1. $11^2$

  2. $12^2$

  3. $10^2$

  4. $13^2$

Show answer
Correct Option: B
Explanation:
$S _{n}=\dfrac{n}{2}\left [ 2a+(n-1)d \right ]$
$a =$ First term
$d =$ Common difference
$n =$ number of terms

Given series is an A.P.
with first term $=$ $1$
common difference $=$ $2$
and last term $=$ $23$

Sum $=$ $\dfrac{12}{2}$ $\times$ $(2+11\cdot 2)$ $=$ $12\times12$
Hence, Option B is correct.

Find the value of the following:
$20\times21$

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

  1. 410

  2. 420

  3. 430

  4. 440

Show answer
Correct Option: B
Explanation:

$20\times21$ $=$ $(20+0)$ $(20+1)$

$400+20$ $=$ $420$
Hence, Option B is correct.

Find the value of the following using some identity.

$44 \times 46$

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

  1. $2024$

  2. $2050$

  3. $2040$

  4. None of these

Show answer
Correct Option: A
Explanation:

$44\times46$ $=$ $(40+4)$ $(40+6)$

$1600+240+160+24$ $=$ $2024$
Hence, Option A is correct.

Find the sum of first $8$ odd numbers.

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

  1. $46$

  2. $64$

  3. $72$

  4. $8$

Show answer
Correct Option: B
Explanation:

Sum of first $8$ odd numbers is $1+3+5+7+9+11+13+15=64$

$N=$ Number of odd numbers are $8$, so $8^2 = 64$

Therefore, B is the correct answer.

Find the value of the following using multiplication pattern.

$29 \times 31$

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

  1. $866$

  2. $799$

  3. $699$

  4. $899$

Show answer
Correct Option: D
Explanation:

$29\times31$ $=$ $(30-1)$ $(30+1)$

$900-1$ $=$ $899$
Hence, Option D is correct.

The resultant of $16\times 18 $ is 

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

  1. $248$

  2. $288$

  3. $268$

  4. None of these

Show answer
Correct Option: B
Explanation:

$16\times18$ $=$ $(20-4)$ $(20-2)$

$400-40-80+8$ $=$ $288$
Hence, Option B is correct.

When we combine two consecutive triangular numbers, we get a __________.

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

  1. square number

  2. consecutive number

  3. non square number

  4. zero

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Correct Option: A
Explanation:

Triangular numbers are obtained by continued summation of natural numbers $1,2,3,4,5,6,7,.....$ 

$\therefore$ Set of triangular numbers is $1,3,6,10,15,21,28.....$
When we add two triangular numbers we get a Square number. 

For example, $1+3=4=2^2$,   $3+6=9=3^2$,   $6+10=16=4^2$ and so on.....
Hence, option A is correct.

Evaluate $22\times 24$ using even-even pattern

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

  1. $428$

  2. $528$

  3. $628$

  4. None of these

Show answer
Correct Option: B
Explanation:

$22\times 24=(20+2)$$\times$$(20+4)$ 

$=$ $400+80+40+8$ $=$  $528$
Hence, Option B is correct.

Find the value of $19 \times 21$ using odd-even property.

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

  1. 399

  2. 299

  3. 199

  4. None of these

Show answer
Correct Option: A
Explanation:

$19\times 21=(20-1)$ $\times$ $(20+1)$ 

$=$ $400$ $+20-20-1$ $=$ $399$
Hence, Option A is correct.