Tag: some special sequences

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Questions Related to some special sequences

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

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

  1. $11^2$
  2. $12^2$
  3. $10^2$
  4. $13^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. square number

  2. consecutive number

  3. non square number

  4. zero
Reveal answer Fill a bubble to check yourself
A Correct answer
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.